ISRO2012-ECE Probability

Question

Person $\text{X}$ can solve $80\%$ of the ISRO question paper and Person $\text{Y}$ can solve $60\%.$ The probability that at least one of them will solve a problem from the question paper, selected at random is :

a. $0.48$
b. $0.70$
c. $0.88$
d.$ 0.92$

Answer 1

P(X) = 0.8

P(Y) = 0.6

P(X ∩ Y) = 0.8 * 0.6 = 0.48 (since x and y are independent events)

P(X ∪ Y ) = P ( X) + P (Y) - P ( X ∩ Y)

                = 0.8 + 0.6 - 0.48 = 0.92

Answer 2

The probability that atleast one of them solves a problem given in question paper
=  1- Probability (both of them not able to solve that problem)
= 1-(Probability that choosen problem does not lie in region which both of them could solve)
$=1-0.2*0.4 \\ = 1 - 0.08 \\ = 0.92$

Answer 3

P(X U Y) = P(X) + P(Y) - P(X)P(Y) bcoz the event of X and Y are independent, so the answer is 1.4 - 0.48 = 0.92 (option D)

Answer 4

Option d is right.

Many ways we can solve this question.