1. Suppose a fair coin is tossed 5 times. (a) What is the probability that we observe the sequence H,T, H, H,T? (b) What is the probability that we observe exactly 3 heads? (c) If we know that 3 heads were obtained in 5 tosses, what is the probability of the sequence H, T, H, H, T?

Q: Two numbers are drawn successively at random with replacement from the set {0, 1, 2, 3, 4, 5, 6, 7,…

A: s : {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. select with replacement E : two numbers are same P(E) = ?

Q: (b) How many bit strings of length 12 have exactly 6 0's? (c) What is the probability that a bit…

A: (b) The total number of bit strings of length 12 have exactly 6 0's is computed as follows. 126=924…

Q: Birthday paradox: Given N people, calculate the probability that at least two people have their…

A:

Q: A box consists of 6 Red balls, 4 Black balls, 7 Blue balls, and 3 White balls. If we conduct the…

A: Given box consists ,6 red balls, 4 black balls, 7 blue balls and 3 white balls.So total balls =…

Q: a fair coin is tossed 10 times find the probability of  (a) exactly six head  (b) at least six heads…

A: When a coin is tossed the probability of getting heads is 1/2 and probability of getting tails is…

Q: 3. You roll a fair six-sided die three times. What is the probability that you roll three different…

A: here six sided die roll three time   so, above is sample space.   here suppose , event A : Roll…

Q: A fair coin is flipped 3 times. What is the probability that (a) the first flip was heads given that…

A: Given: Number of coins flipped = 3 Probability of head on a coin = 12

Q: if (a) the ball selected is not returned to the bin before the next ball is selected and (b) the…

A: Bin containing 50 balls labeled with the numbers 1, 2, ... ,50 . SO Total 50 balls in bin.…

Q: 3. A fair coin is tossed four times, and the sequence of heads and tails is observed. a) List each…

A: A = {at least 3 heads}B = {at most 2 heads}C = {heads on the third toss}D = {1 head and 3 tails}

Q: What is the likelihood that the fourth ball drawn from the bag is the third red ball in the…

A: We  have 3 red (R) balls and 5 yellow (Y) balls in the bag.Balls are drawn one by one without…

Q: Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum…

A:

Q: Suppose you have 7 coins in your pocket: 4 dimes and 3 quarters. 2 coins are selected simultaneously…

A: Solution: From the given information, there are 4 dimes and 3 quarters. Total number of coins is 7.

Q: . On average, three new accounts are opened per day at an Imperial Saving Bank branch. Find the…

A: (a)   Obtain the probability that on a given day the number of new accounts opened at this bank will…

Q: 6. A bag containing different colored balls has a random ball selected from it. If there are 7 red…

A:

Q: A bag contains 3 nickels, 5 dimes, and 4 quarters. If you draw 3 coins at random from the bag,…

A: It is given that  Nickels coins = 3 Dimes coins = 5 Quarters coins = 4 Total coins = 12

Q: An experiment consists of rolling a die until a 3 appears. List the elements of an event E, that…

A: Solution-: List the elements of an event E, that event that 3 appears before the fifth roll.

Q: A committee of 5 is to be selected from a group of 6 men and 9 women. Suppose the selection is made…

A: A committee of 5 is to be selected from a group of 6 men and 9 women.

Q: Suppose we have k people and n seats, with n > k. What is the probability that people will occupy k…

A: Given that, k people and n seats, with n > k.

Q: If n is even and n pennies are tossed high into the air, what is the probability that exactly half…

A: n is even and n pennies are tossed high into the air.