67. Suppose that P(B) = 0.4, P(A|B) = 0.1 and P(A|B^c) = 0.9 (a) Calculate P(A)...

67. Suppose that P(B) = 0.4, P(A|B) = 0.1 and P(A|B^c) = 0.9

(a) Calculate P(A)

(b) Calculate P(A|B)

71. Suppose a couple decides to have three children. Assume that the sex of each child is independent, and the probability of a girl is 0.48, the approximate figure in the US.

(a) How many basic outcomes are there for this experiment? Are they equally likely?

(b) What is the probability that the couple has at least one girl?

104. A multiple-choice quiz has 12 questions, each of which has 5 choices. To pass you need to get at least 8 of them correct. Nina forgot to study, so she simply guesses at random.

Let the random variable X denote the number of questions that Nina gets correct on the quiz. What kind of random variable is X? Specify all parameter values.
Calculate the probability that Nina passes the quiz.

Expert Solution

orchestra answered 2 years ago

If P(A)=0.8, P(B)=0.5, and P(C)=0.4, find P(A ∩ (Bc ∪ Cc )) if A, B, and...

If P(A)=0.8, P(B)=0.5, and P(C)=0.4, find P(A ∩ (Bc ∪ Cc )) if A, B, and C are independent.

A B C Prob Outcome % Prob Outcome % Prob Outcome % 0.4 3 0.1 5...

A B C Prob Outcome % Prob Outcome % Prob Outcome % 0.4 3 0.1 5 0.1 5 0.3 4 0.2 6 0.1 7 0.1 6 0.1 8 0.2 8 0.1 7 0.2 9 0.2 9 0.1 9 0.4 10 0.4 11 Using the following information, which investment would be most preferred using Roy's safety first criterion, if RL=7%. Either B or C (indistinguishable) Only B Only A Either A or B (indistinguishable) Only C Either A or C (indistinguishable)

If P (A) = 0.8, P (B) = 0.5 and P (B|A) = 0.4, what is the value of P (A ∩ B)?

Find the eigenvalues and eigenvectors of the given matrix. ((0.6 0.1 0.2),(0.4 0.1 0.4), (0 0.8...

Find the eigenvalues and eigenvectors of the given matrix. ((0.6 0.1 0.2),(0.4 0.1 0.4), (0 0.8 0.4))

Let A and B be events with P(A) = 0.5, P(Bc ) = 0.4, P(Ac ∩...

Let A and B be events with P(A) = 0.5, P(Bc ) = 0.4, P(Ac ∩ Bc ) = 0.3. (a) Calculate P(A ∪ B), P(A ∩ B), P(B|(A ∪ B)), and P(Ac |B). b) Are A and B independent? Explain why.

9.2.8 Find the steady-state vector for the transition matrix. 0.6 0.1 0.1 0.4 0.8 0.4 0...

9.2.8 Find the steady-state vector for the transition matrix. 0.6 0.1 0.1 0.4 0.8 0.4 0 0.1 0.5

Let A and B be two events in a sample with P(A)=0.4 and P(AuB)=0.7.Let P(B)=p a)i...

Let A and B be two events in a sample with P(A)=0.4 and P(AuB)=0.7.Let P(B)=p a)i For what value of p are A and B mutually exclusive? ii for what value of p are A and B independent? b) Assume that P(A)=0.4 and P(B)=0.3 i find P(B') ii if A and B are mutually exclusive , what is P(A or B) ii given that P(A or B)=0.6, Find the P(B/A) c) suppose events A and B are such that P(A)=0.25,P(B)...

Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.2 0.1 0.2 0.1 0.4...

Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.2 0.1 0.2 0.1 0.4 Step 2 of 5 : Find the variance. Round your answer to one decimal place. Step 3 of 5 : Find the standard deviation. Round your answer to one decimal place.

2. If P(A) = 0.4 and P(B) = 0.6, which of the following must be TRUE?...

2. If P(A) = 0.4 and P(B) = 0.6, which of the following must be TRUE? Select one: A. Events A and B are collectively exhaustive. B. None of the other three choices must be true. C. Events A and B are mutually exclusive. D. Events A and B are statistically independent. 3.A researcher reported that the 95% confidence interval for the mean ranged from 460 to 540. He knew that the population is normally distributed. He was sure that...

P(A) = 0.78, P(B) = 0.75, P(C) = 0.18, P(A∩B) = 0.67, P(A∩C) = 0.15, P(B∩C)...

P(A) = 0.78, P(B) = 0.75, P(C) = 0.18, P(A∩B) = 0.67, P(A∩C) = 0.15, P(B∩C) = 0.12, P(A∩B∩C) = 0.11. Find: 1. Find P(A∪B∪C) 2. Find P((A∩B)∪C) 3. Find P(A∩(B∪C))

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