An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Determine the event that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is less than 4.

Q: We roll a pair of dice four times. Find the probability that a total of five is rolled each time.

A: roll a pair of dice four times  P(total of five each times) = ?

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: Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced…

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Q: Two dice are thrown. Find the probability that the sum of the numbers coming up on them is 9, if it…

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Q: Each of the questions in this box pertains to rolling a pair of fair dice. Find the probability…

A: For each dice, there are 6 possible outcomes. So when two dice are rolled then the possible number…

Q: Suppose you roll two fair dice, one that is red and other is blue. Each die can have numbers from 1…

A: The total number of possible outcomes for rolling two fair dice is 36. The possible outcomes for…

Q: A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 12…

A: roll pair of dice twice.  roll dice : {1,2,3,4,5,6} for rolling pair of dice : total outcomes = 36

Q: A person takes at random one of the numbers 1, 2 or 3, with equal probability each of them, and then…

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Q: You roll a fair six-sided die twice. Find the probability of rolling a 1 the first time and a number…

A: We can roll 1 in only 1 way.For a die there are 6 possible outcomes.So, the probability of rolling a…

Q: 100 people each have a probability of 0.01 of contracting a disease. What is the probability that…

A: Let the random variable X denote the no. of people contracting a disease and it follows binomial…

Q: John rolled a pair of dice. What is the probability that they would sum to 6?

A: In general, there are 36 possible outcomes when rolled a pair of balanced dice.

Q: When rolling a pair of dice, find the probability of getting a sum of 5

A: Given : Sample space of rolling a pair of dice : S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),…

Q: A pair of dice is rolled. Find the probability that the sum of the two dice is 10 or higher

A: A pair of dice is rolled.

Q: if a pair of dice are rolled what is the probability of the number adding up to ten.

A: If a pair of dice are rolled what is the probabilty number addind upto ten  = ?

Q: Find the probability of getting a sum of 6 on two dice if the first die is already shows a 3.

A: Probability : Probability could be a discipline of arithmetic involved with numerical explanations…

Q: Steve has 12 biscuits in a tin. There are 5 digestive and 7 chocolate biscuits. Steve takes two…

A: Given that, Total number of biscuits = 12 5 digestive biscuits and 7 chocolate biscuits We to find…

Q: a coin and a dice roll together six consecutive times. What is the probability of encountering for…

A: Given: Number of rolls = 6 Number of faces in a dice = 6 The sample space in one roll = (H1, H2, H3,…

Q: Three balls are selected randomly from a bag containing 4 red balls and 7 blue ones. Find the…

A: From the provided information, Red balls = 4 Blue balls = 7 Total balls = 11

Q: Two pair of dice are rolled. What is the probability that the sum of their faces will be equal to…

A: Given: Two pair of dice are rolled. To find : The probability that the sum of their faces will be…

Q: A pair of dice are tossed twice.Find the probability that the first roll is a total of at least 11…

A: The objective of this question is to find the probability of two independent events happening. The…

Q: You have a 30-sided dice. Your friend Hugo has three favorite numbers: 5, 3, and 10. What is the…

A: Given You have a 30-sided dice. Your friend Hugo has three favorite numbers: 5, 3, and 10.

Q: In a Roulette game, a ball falls onto a spinning wheel and randomly ends up in one of 37 pockets.…

A: Given the experiment of the Roulette game, a ball falls onto a spinning wheel and randomly ends up…

Q: find the probability that the sum of the 2 dice is an even number or a number less than 5

A: When two dice are thrown then these following cases occur  sum Outcomes Number of outcomes…

Q: A pair of dice are tossed twice. Find the probability that both rolls give at most a sum of 6.

A: We have given that,  A pair of dice are tossed twice then the sample space (S) is,  S = {(1,1),…

Q: Find the probability distribution for the sum of the three sides.

A: Given,  Number of dice = 3 Number of sides with different number on each dice = 4 Total number of…

Q: You roll a die five times. What is the probability that you will see a string of three or more…

A: Given data: *The die is rolled 5 times, n=5. The probability of getting one (success) when a one die…

Q: Caleb rolls two regular six sided dice determine the odds against him rolling an odd or a sum of 4

A: Given that Caleb rolls two regular six sided dice we have to find the odds against him rolling an…

Q: In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will…

A: Here, two dice are thrown. Let A denote the event that the dice resulted in a doublet. Let B denote…

Q: We throw three independent fair dice. Find the probability that the sum of the outcomes is equal to…

A: When die is rolled, there would be 6 possible outcomes1,2,3,4,5,6. For drawing three independent…

Q: for the experiment of rolling and ordinary pair of dice, find the probability that the sun will be…

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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.