Question

A telephone survey uses a random digit dialing machine to call subjects. the random digit dialing machine is expected to reach a live person 15% of the time. in eight attempts, what is the probability of achieving exactly two successful calls?

Answer 1

P($r$ successes in $n$ trials) = ⁿ$C_{r}$×$[P(Success)^{r}]$×$[P(failure)]^{n-r}$

We have
$n=8$
$r=2$
$P(Success)=0.15$
$P(Failure)=0.85$

Substitute these values into the formula, we have
P( 2 success in 8 trials) = ⁸C₂ × (0.15)² × (0.85)⁶
P( 2 success in 8 trials) = 0.2376.... ≈ 0.24 = 24%