| A can solve 40% of the problem given in a book and B can solve 70%. What is the probability that atleast one of them will solve the problem selected at random from the book? |
A) 0.95
B) 0.90
C) 0.89
D) 0.97
Correct Answer: D
Solution :
| Let Event X : A solve the problem | |
| Event Y : B solve the problem | |
| Clearly, X and Y are independent events such that | |
| \[P\,\,(X)=\frac{90}{100}=\frac{9}{10}\]\[\Rightarrow \]\[P\,\,(Y)=\frac{70}{100}=\frac{7}{10}\] | |
| \[\therefore \]Required probability, | |
| \[P\,\,(X\cup Y)=1-\overline{P(X)}\,\overline{P(Y)}=1-\left( 1-\frac{9}{10} \right)\left( 1-\frac{7}{10} \right)\] \[=1-\left( \frac{1}{10}\times \frac{3}{10} \right)=\frac{97}{100}=0.97\] |
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