Statistics And Probability Question 235

Question: If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is

[IIT 1989]

Options:

A) 0.5

B) 0.44

C) 0.6

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  •                 Here                                                                                               $ P(X)=0.3; $                                                                                                  $ P(Y)=0.2 $                     Now                                                                          $ P(X\cup Y)=P(X)+P(Y)-P(X\cap Y) $                     Since these are independent events, so                                                                                                                                                                   $ P(X\cap Y)=P(X)\,.\,P(Y) $                                  Thus required probability                                                                                    $ =0.3+0.2-0.06=0.44 $  .