## 5c2 probability

Problem 1 :. A coin is tossed three times.

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Find the probability of getting :. Problem 2 :. A dice is rolled twice. What is the probability of getting a difference of 2 points?

Problem 3 :. Two dice are thrown simultaneously. Find the probability that the sum of points on the two dice would be 7 or more.

Problem 4 :. What is the chance of picking a spade or an ace not of spade from a pack of 52 cards? Problem 5 :. Find the probability that a four digit number comprising the digits 2, 5, 6 and 7 would be divisible by 4. Problem 6 :. A committee of 7 members is to be formed from a group comprising 8 gentlemen and 5 ladies.

What is the probability that the committee would comprise :. Problem 7 :.

### PROBABILITY WORKSHEET

A strabismus surgery has a probability of 0. Use the techniques of tree diagrams to find the probability that the surgery will be successful within two attempts. Problem 8 :. What is the probability of getting :. Solution :. When a coin is tossed three times, first we need enumerate all the elementary events.

This can be done using 'Tree diagram' as shown below :. That is. If we denote the occurrence of 2 heads by the event A and if assume that the coin as well as performer of the experiment is unbiased then this assumption ensures that all the eight elementary events are equally likely.

Then by the classical definition of probability, we have. Let B denote occurrence of at least 2 heads i.

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Find the probability of getting a difference of 2 points. If an experiment results in p outcomes and if the experiment is repeated q times, then the total number of outcomes is pq.A bag contains tickets numbered 1, 2, 3, … If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?

Now left most place is fixed in 8 ways.

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Units place is filled with 9 ways. Total 72 numbers. In how many ways a team of 11 must be selected a team 5 men and 11 women such that the team must comprise of not more than 3 men.

Four people each roll a four die once. Find the probability that at least two people will roll the same number? None of the given choices d.

In a single throw with two dice, find the probability that their sum is a multiple either of 3 or 4. A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?

We have to multiply two probabilities. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black. There are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red? And this is a case of replacement. From a bag containing 8 green and 5 red balls, three are drawn one after the other. There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls.

A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.Evaluate each expression.

Medications for Depression A researcher wishes her patients to try a new medicine for depression. How many different ways can she select 5 patients from 50 patients?

Selecting Players How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players? Coffee Selection A coffee shop serves 12 different kinds of coffee drinks. How many ways can 4 different coffee drinks be selected? Selecting Christmas Presents If a person can select 3 presents from 10 presents under a Christmas tree, how many different combinations are there?

Buffet Desserts In how many ways can you choose 3 kinds of ice cream and 2 toppings from a dessert buffet with 10 kinds of ice cream and 6 kinds of toppings?

Bridge Foursomes How many different tables of 4 can you make from 16 potential bridge players?

How many different tables if 4 of the players insist on playing together? Questions are typically answered in as fast as 30 minutes. Q: An oil company estimates that only 1 well in 24 will yield commercial quantities of oil.

Assume that A: According to the provided data, the number of trials, n is An oil company estimates that only Q: Evaluate the given expression P 7, 6. A: The random variable X follows geometric distribution with probability 0.

The geometric distributi Q: A firm has two computer systems available for processing telephone orders. At any given time, system A: It is given that the probability of system A being down is 0. Also the probability of system B be A: The probability that exactly 3 of them do not require a vision correction is obtained below:Here, do Q: Consider the probability distribution of a random variable x.

Is the expected value of the distribut A: The expected value is not necessarily one of the possible values of X.A group of 3 female student and 5 male students are available to fill certain student government posts. If 4 students are to be randomly selected from this group, find the probability that exactly 2 female students will be chosen among the 4 chosen.

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To solve this problem, we want to know out of those ways, how many of them contain 2 males and 2 females. If anything is unclear, please request for a clarification before rating this answer. I located some sample problems with solutions online to make sure that my method is correct. Search terms: committee answer chosen probability "A group of" "consists of" "randomly selected" "find the probability".

Regards, secretga. Excuse me, but I think there is an error here. The previous comment is correct. Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice.

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Basically, it shows how many different possible subsets can be made from the larger set. For this calculator, the order of the items chosen in the subset does not matter. Also referred to as r-combination or "n choose r" or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k. You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6.

How many different combinations of 2 prizes could you possibly choose? In this example, we are taking a subset of 2 prizes r from a larger set of 6 prizes n. A teacher is going to choose 3 students from her class to compete in the spelling bee.

She wants to figure out how many unique teams of 3 can be created from her class of In this example, we are taking a subset of 3 students r from a larger set of 25 students n.

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A restaurant asks some of its frequent customers to choose their favorite 4 items on the menu. If the menu has 18 items to choose from, how many different answers could the customers give? Here we take a 4 item subset r from the larger 18 item menu n. First, let's find the total handshakes that are possible. That is to say, if each person shook hands once with every other person in the group, what is the total number of handshakes that occur? A way of considering this is that each person in the group will make a total of n-1 handshakes.

Since there are n people, there would be n times n-1 total handshakes. In other words, the total number of people multiplied by the number of handshakes that each can make will be the total handshakes. However, this includes each handshake twice 1 with 2, 2 with 1, 1 with 3, 3 with 1, 2 with 3 and 3 with 2 and since the orginal question wants to know how many different handshakes are possible we must divide by 2 to get the correct answer.

The order of the items chosen in the subset does not matter so for a group of 3 it will count 1 with 2, 1 with 3, and 2 with 3 but ignore 2 with 1, 3 with 1, and 3 with 2 because these last 3 are duplicates of the first 3 respectively.

Discrete Math. Combinations Calculator nCr. Combinations nCr Calculator. Report a Problem. Get a Widget for this Calculator. Follow CalculatorSoup:.It is necessary to follow the next steps: Enter the total number of objects and sample size in the box. These values must be positive integers; The second must be less than the first one. What is the formula for Permutation?

The field of mathematics which studies different possibilities for the arrangement of objects is called combinatorics. For example, if we buy three different books in a different order, how many elements would the corresponding sample space have?

What is Combination? For example, Ann has five coins in his bag and pulls out three at one time. How many different amounts can she get? The grade school students may use this permutation and combination calculator to generate the work, verify the results of the combinatorics, probability and statistical problems or do their homework problems efficiently.

The users may refer the below table for quick reference to check what are all the permutations and combinations for n distinct objects taken r at a time. To verify the calculation, use the above nPr and nCk calculator.

Example Problem 3 How many 4 digit numbers can be formed using 4 digits? The use of permutations and combinations in mathematics and computer science is huge. Especially, they are often mentioned in graph theory, probability, geometry, etc. Discrete mathematics is one of the most important field in computer science. There are so many applications to graph theory, for example, Facebook uses many concepts of graph theory. In how many ways can they select a chairperson, vice-chairperson and secretary, if one person cannot hold more than one office?

Six will be selected to form a team. How many different teams of 6 can be formed? The permutation and combination calculator, formula, example calculation work with stepsreal world problems and practice problems would be very useful for grade school students K education to understand the main concept of combinatorics.

This concept can be of significance in many fields of science and real life. Permutation and Combination Calculator. Permutations - nPr Combinations - nCr.

Permutations and Combinations - Formulae - Don't Memorise - GMAT/CAT/Bank PO/SSC CGL

Combinations n-CHOOSE-k nCk 2 choose 1 2 2 choose 2 1 3 choose 1 3 3 choose 2 3 3 choose 3 1 4 choose 1 4 4 choose 2 6 4 choose 3 4 4 choose 4 1 5 choose 1 5 5 choose 2 10 5 choose 3 10 5 choose 4 5 5 choose 5 1 6 choose 1 6 6 choose 2 15 6 choose 3 20 6 choose 4 15 6 choose 5 6 6 choose 6 1.PINNACLE - accept very large stakes.

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### How to work out 4C2...?

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