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

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is almost 0.3. Is it possible that the probability of B getting selected is 0.9?

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is almost 0.3. Is it possible that the probability of B getting selected is 0.9?

Grade:10

3 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago

Hello Student,
Please find the answer to your question
Let A denote the event that the candidate A is selected and B the event that B is selected. It is given that
P (A) = 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
P (A ∩ B) ≤ 0.3 . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Now, P (A) + P (B) - P (A ∩ B) = P (A ∪ B) ≤ 1
Or 0.5 + P (B) - P (A ∩ B) ≤ 1 [Using (1)]
Or P (B) ≤ 0.5 + P (A ∩ B) ≤ 0.5 + 0.3 [Using (2)]
Or P (B) ≤ 0.8 ∴ P (B) can not be 0.9

Thanks
Jitender Pal
askIITians Faculty

Rahul Jain
13 Points
4 years ago
Please confirm, what’s wrong in this?
P(A and B) = P(A) × P(B)
0.3 = 0.5 × P(B)
P(B) = 0.3/0.5 = 0.6
 
Rahul Jain
Rishi Sharma
askIITians Faculty 646 Points
8 months ago
Dear Student,
Please find below the solution to your problem.

Let A denote the event that the candidate A is selected and B the event that B is selected.
It is given that P (A) = 0.5 . . . (1)
P (A ∩ B) ≤ 0.3 . . . . . (2)
Now, P (A) + P (B) - P (A ∩ B) = P (A ∪ B) ≤ 1
0.5 + P (B) - P (A ∩ B) ≤ 1 [Using (1)]
P (B) ≤ 0.5 + P (A ∩ B) ≤ 0.5 + 0.3 [Using (2)]
P (B) ≤ 0.8
∴ P (B) can not be 0.9

Thanks and Regards

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