Question

A, B, C take one shot each at a target. Their probabilities of hitting the target are respectively 0.4, 0.5 and 0.8. The probability that at least two of them hit the target, is

• A. $\frac{13}{25}$
• B. $\frac{9}{25}$
• C. $\frac{3}{5}$
• D. None of these

Answer 1

Answer: (C)

$\frac{3}{5}$

Let the desired event be called E
Also let A,B and C hitting the target be called A,B and respectively and missing the target be called $\overline{A},\overline{B}and\overline{C}$
$P\left(E\right)=P\left(A\right)P\left(B\right)P\left(C\right)+P\left(\overline{A}\right)P\left(B\right)P\left(C\right)+P\left(A\right)P\left(\overline{B}\right)P\left(C\right)+P\left(A\right)P\left(B\right)P\left(\overline{C}\right)\Rightarrow P\left(E\right)=0.4\times 0.5\times 0.8+0.6\times 0.5\times 0.8+0.4\times 0.5\times 0.8+0.4\times 0.5\times 0.2=0.16+0.24+0.16+0.04=0.6=\frac{3}{5}$