Answer:
Step-by-step explanation:
We would apply the formula for binomial distribution. It is expressed as
P(x = r) = nCr × q^(n - r) × p^r
Where
p represents probability of success
q represents probability of failure.
n represents number of sample.
From the information given,
p = 10% = 10/100 = 0.1
q = 1 - q = 1 - 0.1 = 0.9
n = 8
1)The probability that none fails is
P(x = 0) = 8C0 × 0.9^(8 - 0) × 0.1^0
P(x = 0) = 0.43
2) The probability that one fails is
P(x = 1) = 8C1 × 0.9^(8 - 1) × 0.1^1
P(x = 1) = 0.38
3) The probability that four fails is
P(x = 4) = 8C4 × 0.9^(8 - 4) × 0.1^4
P(x = 4) = 0.0046
3) The probability that six fails is
P(x = 6) = 8C6 × 0.9^(8 - 6) × 0.1^6
P(x = 6) = 0.00002268
4) The probability that eight fails is
P(x = 8) = 8C8 × 0.1^(8 - 8) × 0.1^8
P(x = 8) = 0.00000001
