For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1 st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.

Question

Aditi Chauhan · Answer

Hello Student,

Please find the answer to your question

Let us consider

E₁ ≡ event of passing I exam

E₂ ≡ event of passing II exam

E₃ ≡ event of passing III exam

Then a student can qualify in anyone of following ways

1. He passes first and second exam.

2. He passes fires, fails in second but passes third exam.

3. He fails in first, passes second and third exam.

∴ Required probability

= P (E₁) P (E₂| E₁) + P (E₁) P (E₂| E₁) P (E₃| E₂) + P (E₁) P (E₂| E₁) P (E₃| E₂)

[as an event is dependent on previous one]

= p. p + p. ((1 – p). p/2 + (1 – p) p/2 p

= p² + p²/2 – p³/2 + p²/2 – p³/2 = 2p² – p³

Thanks
Aditi Chauhan
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For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1 st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1^st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.

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For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1 st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.

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For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1^st exam is p. If he fails in one of the exams then the probability of passing in the next exam is p/2 otherwise it remains the same. Find the probability that he will qualify.