A can solve 90% problems and B can solve 70% problems of the book. A problem is selected at random from the book. The probability that the problem is solved, is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.97 **
$P(A)=0.9,\; P(B)=0.7$
$P(\text{solved})=P(A)+P(B)-P(A)P(B)$
$=0.9+0.7-(0.9)(0.7)$
$=1.6-0.63$
$=0.97$
The probability that the selected problem is solved is $0.97$.