Answer to Question #191118 in Statistics and Probability for ROWEL RIN TACAL

Question

1. In a box having 6 light switches, the probability of having a defective switch is 0.3 and the probability of having no defective switch is 0.6. Find the probability that there is at most 1 defective light switch in a box. 

Answer 1

We have given that,

$n = 6$

$p = 0.3$

$q = 0.7$

We have to find the probability that there is at most 1 defective light switch in a box

Using the binomial distribution:

$P(X) = ^nC_r(p)^r(q)^{n-r}$

$P(X\le 1) = P(X=0)+P(X=1)$

$= ^6C_0(0.3)^0(0.7)^2+ ^6C_1(0.3)^1(0.7)^1$