Three students, A, B and C can respectively solve 50%, 25% and 20% of the problems in a book. A particular problem is selected at random from the book. The probability that at least one of them will solve the problem is

$\frac{7}{10}$

The correct answer is Option (3) → $\frac{7}{10}$ **

Let total probability of solving a problem by A, B, and C be:

$P(A) = 0.5,\ P(B) = 0.25,\ P(C) = 0.2$

Assuming independence, probability that none solve it:

$P(\text{none}) = (1 - 0.5)(1 - 0.25)(1 - 0.2) = (0.5)(0.75)(0.8) = 0.3$

Hence, probability that at least one solves it:

$P(\text{at least one}) = 1 - P(\text{none}) = 1 - 0.3 = 0.7$

Final Answer:

$P = 0.7$