Question

Person A can solve \(90\%\) of the problems given in the book and Person B can solve \(70\%\). Then the probability that at least one of them will solve the problem selected at random from the book is:

• A. \(0.16\)
• B. \(0.69\)
• C. \(0.97\)
• D. \(0.20\)

Hint:

For probability questions involving "at least one", it is usually easier to use the complement rule: \[ P(\text{at least one}) = 1-P(\text{none}) \] This method avoids lengthy calculations.

Answer 1

The Correct Option is C

Step 1: Use the complement rule.
\(P(\text{at least one solves}) = 1 - P(\text{neither solves})\). \(P(A \text{ fails}) = 0.10\), \(P(B \text{ fails}) = 0.30\).

Step 2: Compute.
\[P = 1 - 0.10 \times 0.30 = 1 - 0.03 = 0.97.\]
\[\boxed{0.97}\]