Suppose you roll 2 dice. What is the pobability that the sum of the 2 dice is exactly 4, given that the 1st dice is a 1?

Q: Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the…

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Q: For this problem, assume there are 6 grey females, 4 grey males, 5 white females, and 6 white males.…

A: Let A be the event that the both mice are males Let B be the event that the both mice are grey…

Q: For this problem, assume that the committee contains 10 men and 5 women and that three are selected…

A: There are 10 men and 5 women. So total (10+5)=15 persons are there. We can pick any 3 persons from…

Q: A problem in statistics is given to three students whose chances of solving are 2, and 4…

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Q: For this problem, assume that the committee contains 10 men and 8 women and that three are selected…

A: Given that, A committee consists of 10 men and 8 women Three members are selected at random for a…

Q: Suppose the defendant in a particular judicial system is presumed guilty until proven innocent.…

A: Null and alternative hypotheses: The hypothesis which is tentatively fixed up under and tested for…

Q: Suppose, you are attending an exam where there are 9 multiple choice questions with 3 options in…

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Q: You are rolling two dice, what are your chances of winning If the two dice should have an equal…

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Q: John plans to toss a die until he observes two even numbers. What is the chance that the 2nd even…

A: For a dice roll the sample space is given by: S=1,2,3,4,5,6 so the probability of getting odd number…

Q: A has six shares in the lottery in which there are three prizes and ten blanks. B has two shares in…

A: Solution is given:

Q: Suppose there are three desks, each with two drawers. One desk contains a gold medal in each drawer,…

A: Given, There are three desks, each with two drawers. One desk contains a gold medal in each drawer,…

Q: Barbie has applied to both Harvard and Yale. The probability that Harvard will admit her is 0.65,…

A: We denote Yale by Y, Harvard by H, and thus their corresponding probabilities by P(Y) and P(H),…

Q: Consider the following game with two dice (red and blue). The rules for the game are as follows:…

A: Given information: The game is conducted by rolling two dice.

Q: Suppose you play a game where you toss three fair coins. If you get three tails, you win $10.…

A: Probability of getting a tail while tossing a coin is 1/2 So, if 3 coins will be tossed then the…

Q: The probability of event Ac is .4, the probability of (A U B)c is .1, and the probability of the…

A: Given Data: The probability of event Ac is: P(Ac)=0.4 The probability of event (AUB)c is:…

Q: What is the probability of success on each trial?

A:

Q: Suppose, you are rolling two regular six-sided dice and two four-sided dice together. Let’s say, the…

A: Sample space for rolling a two six-sided dice: Ω1=1,1, 1,2, 1,3, 1,4, 1,5, 1,6,2,1, 2,2, 2,3, 2,4,…

Q: Suppose that two dice are rolled, a red one and a white one, specify each event. a) The sum of the…

A: Given that two dice are rolled, a red one and a white one, specify each event. We find the events…

Q: Ian rolls the two dice and will win the game if the sum of the numbers of the two dice is 8. What is…

A: Two dice are rolled, outcome of this event is: Ω= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),…

Q: A has four shares in a lottery in which there are four prizes and five blanks. B has three shares in…

A: Solution:

Q: For this problem, assume that the committee contains 7 men and 9 women and that three are selected…

A:

Q: As you entered a casino, an oversized gold bowl containing four dice is presented to you. Pick one…

A: The term probability is defined as the chance of occurrence of an event. The probability value…

Q: Suppose, you are rolling two regular six-sided dice and two four-sided dice together. Let's say, the…

A: Let 'S1' be the sample space of rolling two six-sided dice together. S1={1, 1, 1, 2, 1, 3, 1, 4, 1,…

Q: You roll 2 fair dice, one green and one red. Are the outcomes on the dice independent.

A: Given that, Roll a  2 fair dice, one green and one red.

Q: As you entered a casino, an oversized gold bowl containing four dice is presented to you. Pick one…

A: We proceed to solve the problem by splitting it into cases.  Also, we have conditional probability:…

Q: If you toss four coins together at the same time, what's the probability of getting all "heads"? You…

A: Given: For unbiased coin,  p(head) = p(tails) = 0.50 Number of coin tosses = 4

Q: If you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the…

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Q: In monopoly, a player rolls two 6-sided dice and moves the sum of the values shown. If it's your…

A: The player rolls a two 6-sided dice and moves the sum of the values shown. If it's your turn to roll…

Q: In rolling the dice two times, the probability that the sum of the two appearing numbers is greater…

A: when we roll a dice twice the total possible outcomes is 36 which is given by (1,1),…

Q: The probability of A is 0.60, the probability of B is 0.45, and the probability of either is 0.80.…

A: Given:PA=0.6PB=0.45PA∪B=0.8

Q: Ruth tells you that when you roll a pair of fair dice, the probability of obtaining a pair of…

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Q: The probability of A is 0.60, the probability of B is 0.45, and the probability of both is 0.30.…

A: Given: P(A)=0.60 P(B)=0.45 probability of both = P(A∩B)=0.30

Q: if you toss a fair coin 8 times, what is the probaility of getting all heads

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Q: If the probability of a student taking a calculus class is 0.10, the probability of taking a…

A: According to the provided information, the probability of a student taking a calculus class is 0.10.…

Q: How many ways can you roll 2 dice so that the sum of the dots is either 7 or 11?

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Q: Suppose that we roll two fair six-sided dice and record the numbers showing as an ordered pair. Let…

A: Difference between the two numbers is denoted by Y. There can be 6 possible values of Y. There are…

Q: Suppose E= "sum is 5" and F= "exactly one of the dice is even". Are E and F independent?

A: The sample space is  S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)…

Q: You are one space short of winning a baord game and must roll a 1 on a die to claim victory. You…

A: Statistical simulation is an artificial way to generate data. This generated data can be used for…

Q: When throwing the dice, if the number of points shown is 1,2,3, he wins 200 dinars, and if the…

A: Probability

Q: Now suppose we only care about sum of the dice. What are the different outcomes and their…

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Q: For this problem, assume there are 5 grey females, 6 grey males, 4 white females, and 5 white males.…

A: It has been given that there 5 grey females and 6 grey males, 4 white females and 5 white males.…

Q: Suppose, you are rolling two regular six-sided dice and two four-sided dice together. Let's say, the…

A: Given, Number of outcomes of two regular six sided outcomes = 36 Number of outcomes of two regular…

Q: There are three dice rolled at the same time. a. How many possible outcomes are there if the sum of…

A: Given that, three dice are rolled at the same time.

Q: How many rolls of two dice are needed so that the probability of rolling a double six within this…

A: Given, number of die, n=2 total number of ways=36 The binomial distribution formula is…

Q: For this problem, assume there are 6 grey females, 6 grey males, 4 white females, and 3 white males.…

A:

Q: uppose a standard six-sided die is rolled and you receive $5.50 for every dot showing on the top of…

A: When a six-sided die is rolled the probability of getting each number is 1/6.  1 dot is present In…

Q: Two diced are tossed 216 times. How many times would you expect to get a sum of 4?

A: It is given that, the number of times the two dice are tossed (n) is 216.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.