The probability that Jack passes calculus II given that he passes Calculus I is
ID: 3201333 • 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 Calcullus 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.
Explanation / Answer
Solution:-
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
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