Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
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
askIITians Faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free