Question

When a substance is synthesized under laboratory conditions, the probability of an

explosion in a separate experiment is p = 0.02. Determine the probability that in a series of 10

syntheses: 1) the explosion will occur three times; 2) the explosion will not occur

Answer 1

$n=10 \\ p = 0.02 \\ q = 1 -0.02 = 0.98 \\ P(X=x)=C(n,x)p^x q^{n-x}$

1) the explosion will occur three times

$P(X=3) = \frac{10!}{3!(10-3)!} \times 0.02^3 \times 0.98^{10-3} = 0.000833$

2) the explosion will not occur

$P(X=0) = \frac{10!}{0!(10-0)!} \times 0.02^0 \times 0.98^{10-0} = 0.817072$