If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and n-x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor selects six numbers from 1 to 60 (without repetition), and a winning six-number combination is later randomly selected. Find the probabilities of getting exactly three winning numbers with one ticket. (Hint: Use A = 6, B = 54, n = 6, and x = 3.) P(x) = A! (A-x)!x! B! (B-n+x)!(n-x)! + (A + B)! (A+B-n)!n!

Q: P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05. What is P(A and B)?

A: Given that  P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05

Q: Given P(A) = 0.36, P(A and B) = 0.32, P(A or B) = 0.50, what is P(B)? Answer in decimal form.…

A: From the provided information, P(A) = 0.36, P(A and B) = 0.32, P(A or B) = 0.50

Q: Given P(A and B) = 0.02, P(A) = 0.82, what is P(B|A)? Answer in decimal form. Round to 3 decimal…

A: The conditional probability of B given A, denoted P(B|A), is

Q: Given P(A and B) = 0.37, P(B) = 0.57, P(B|A) = 0.91, what is P(A)?

A: We have to find given probability.

Q: Given P(A and B) = 0.16, P(A) = 0.87, what is P(B|A)? Answer in decimal form.  Round to 3 decimal…

A:

Q: Given P(A and B) = 0.02, P(B) = 0.88, P(B|A) = 0.68, what is P(A)?

A: P(A and B) = 0.02  P(B) = 0.88  P(B|A) = 0.68  P(A)=?

Q: If P(A or B)= 0.8, P(A)= 0.5 and P(A and B) = 0.25, find P(B)

A:

Q: If P(A) = 0.7, P(B) = 0.8, and P(A or B) = 0.9, find P(A and B).

A:

Q: Suppose that P(E)=0.76, P(F)= 0.45, and P(E and F) = 0.32. What is P(E or F)? P(E or F) (Simplify…

A:

Q: IfP(A =0.3,P(B)=0.4andP(A and B)=0.7areAandBME?

A: The probabilities of the events are given as follows:

Q: Given P(A and B) = 0.23, P(A) = 0.84, what is P(B|A)?

A:

Q: If P(A) = 0.5 and P(B) = 0.80, then P(A or B) must be 0.95.   TRUE or FALSE

A: From the provided information, P (A) = 0.5 and P (B) = 0.80

Q: Given P(B) = 0.47, P(A and B) = 0.29, P(A or B) = 0.55, what is P(A)?   Answer in decimal form.…

A:

Q: Given P(A) = 0.94, P(B) = 0.98, P(B|A) = 0.52, what is P(A and B)?

A:

Q: Given that P(A AND B)=0.37 and P(A|B)=0.68, what is P(B)?

A: Given, PA∩B=0.37PA|B=0.68

Q: Given P(A and B) = 0.25, P(B) = 0.85, P(B|A) = 0.93, what is P(A)?

A:

Q: 39. What is the value of (EX)² for the scores: -1, 0, 3, 5?

A: Given that  The data are -1,0,3,5 Find the value (∑X)2

Q: Given P(A and B) = 0.10, P(A) = 0.68, what is P(B|A)

A: Given that, P(A and B) = 0.10 P(A) = 0.68

Q: If P(A) = 0.4, P(B) = 0.5, and P(AUB) = 0.7, find P(ANB). P(AUB).

A:

Q: Given P(A) = 0.86, P(B) = 0.77, P(B|A) = 0.37, what is P(A and B)?

A: Let A and B are two events. The known probabilities are, Using the conditional probability formula,…

Q: Given P(A) = 0.16, P(B) = 0.88, P(B|A) = 0.25, what is P(A and B)?

A: Given , P(A) = 0.16, P(B) = 0.88, P(B|A) = 0.25

Q: given that P(A or B) = 1/3, P(A) = 1/7, and P(A and B) = 1/8, find P(B) a. 101/168 b. 159/168 c.…

A: Concept of General Addition Rule: For any two events A and B the General Addition Rule states that:\

Q: Given P(A) = 0.27, P(A and B) = 0.33, P(A or B) = 0.41, what is P(B)? Answer in decimal form.…

A: Formula : P(A or B) = P(A) + P(B) - P(A and B)

Q: Given that p(B│A) =.75 and p(A B) =.28, find p(A).

A: GivenP(B|A)=0.75P(A∩B)=0.28

Q: Given P(A) = 0.80, P(B) = 0.44, P(B|A) = 0.51, what is P(A and B)? Answer in decimal form.  Round…

A: We will use the conditional probability formula

Q: Given P(A) = 0.84, P(B) = 0.44, P(B|A) = 0.20, what is P(A and B)?

A: Solution: From the given information, P(A)=0.84, P(B)=0.44 and P(B|A)=0.20.