Human error is given as the reason for 75% of all accidents in a plant. Use the formula for the binomial distribution to find the probability that human error will be given as the reason for two of the next four accidents.
Answers
Given : Human error is given as the reason for 75% of all accidents in a plant , Use the formula for the binomial distribution
To find : probability that human error will be given as the reason for two of the next four accidents.
Solution:
Human error is given as the reason for 75% of all accidents in a plant
=> P ( human error) = 75/100 = 3/4
Probability ( not human error) = 1 - 3/4 = 1/4
P(x) = ⁿCₓpˣqⁿ⁻ˣ
probability that human error will be given as the reason for two of the next four accidents.
n = 4 & x = 2
= ⁴C₂(3/4)²(1/4)⁴⁻²
= 6 ( 3² / 4⁴)
= 54/256
= 27/128
= 0.21
21 % is the probability that human error will be given as the reason for two of the next four accidents
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