Answer to Question #287893 in Statistics and Probability for Sanjana

Question

Let the probability that the electrocardiograph will require repair during the warranty

period is 0.2. Determine the probability that during the warranty period out of six cardiographs:

1) no more than one will require repair; 2) at least one will require repair

Answer 1

$n=6 \\ p = 0.2 \\ q = 1 -0.2 = 0.8 \\ P(X=x)=C(n,x)p^x q^{n-x}$

1) no more than one will require repair

$P(X≤1) = P(X=0) + P(X=1) \\ = \frac{6!}{0!(10-0)!} \times 0.2^0 \times 0.8^{6-0} + \frac{6!}{1!(6-1)!} \times 0.2^1 \times 0.8^{6-1} \\ = 0.262144 + 0.393216 \\ = 0.65536$

2) at least one will require repair

$P(X≥1) = 1 -P(X<1) \\ = 1 -P(X=0) \\ = 1 - [\frac{6!}{0!(10-0)!} \times 0.2^0 \times 0.8^{6-0}] \\ = 1 -0.262144 \\ = 0.737856$