The probability that Jack passes Calculus II given that he passes Calculus I is
ID: 3201936 • Letter: T
Question
The probability that Jack passes Calculus II given that he passes Calculus I is 0.8. The probability that Jack passes Calculus II given that he fails Calculus I is 0.3. Likewise, the probability that Jack passes Calculus III given that he passes Calculus II is 0.8. The probability that Jack passes Calculus III given that he fails Calculus II is 0.3. Suppose that Jack passes Calculus I. (a) Find the probability that Jack passes Calculus III. (b) Find the probability that Jack passes Calculus II and Calculus III. Show that if P(A) > 0, then P(A BA) greaterthanorequalto P(A BA B). There are two coins: Coin 1 is a fair coin that comes heads with probability 1/2 and tails with probability Coin 2 is a fake coin that comes heads all the time. The following experiment is performed: We choose one of the two coins (Coin 1 or Coin 2) uniformly at random (each coin is chosen with probability and consider two independent tosses of the chosen coin. Let E_1 be the event that the first toss is heads, E_2 be the event that the second toss is heads, and F be the event that the chosen coin is Coin 1. (a) Are E_1 and E^_2 independent? Justify your answer. (b) Are E_1 and E_2 conditionally independent given F? Justify your answer.Explanation / Answer
Solution:-
1)
a) The probability that Jack passes Calculas III is 0.70.
Probability of passing Calculas II = 0.8
Probability of failing Calculas II when he passed calculas I = 1 - 0.8 = 0.2
Proability of passing Calculas III when he passes Calculas II = 0.8 × 0.8 = 0.64
Proability of passing Calculas III when he fails Calculas II = 0.2 × 0.3 = 0.06
Probability of passing calculas III = 0.64 + 0.06 = 0.70
b)The probability that Jack passes Calculas II and Calculas III is 0.64
Probability of passing Calculas II = 0.8
Proability of passing Calculas III when he passes Calculas II = 0.8 × 0.8 = 0.64
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.