Someone is playing roulette until the first win. The probability to win in each

Question

Someone is playing roulette until the first win. The probability to win in each round is p, the probability to is q = 1 - p. Find the probability that this person will play exactly once _______ twice _______ 3 times _______ 6 times _______ n times _______ Express your answer in terms of p and q. Find the conditional probability that there is a boy in a family with two kids if it is known that one of the children is girl _______. Find the conditional probability that there is it boy in a family with two kids if it is known that the first child is a girl _______. A point is randomly chosen in a square [0, 1] times [0, 1]. The event A is that the point is in a square with vertices (0, 0), (0, 1/2), (1/2, 1/2), (1/2, 0). The event B is that the point is in a square with vertices (1/4, 1/4), (1, 1/4), (1, 1), (1/4, 1). (See Fig. 1a). Find the probability^1 P(A) = P(B) = P(AB) = P(A or B) = P(A^e) = P(B^e) = P(A^e and B^e) = P((A or B)^e) = P(A|B) = P (B|A) = Are events A and B independent ? _______ A point is randomly chosen in a square [0, 1] times [0, 1]. The event A is that the point is in square with vertices (0, 0),(0, 1/2), (1/2, 1/2), (1/2, 0). The event B is that the

Explanation / Answer

Dear Student

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Given a roulette wheel with probability of winning defined by p and probability of loosing defined y q.

Now

a) If the person played only 1 match and he leaves only after winning.

=> He won the first match played

Probability = p

b) Twice

=> The person lost his first match and won the second.

Probability = q X p

(By fundamental principle of multiplication, since both the events are happening in consequence hence their probabilities are multiplied.)

c) 3 Times

Person lost first 2 matches and won thrid.

Probability = q^2p

d) 6 Times

Probability = q^5p

e) n times

Probability = q^ (n-1) * p

Solution.

Kindly note that as per chegg policied an expert can answer maximum 1 question at a time. Thank you

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