A study shows that 6% of household appliances fail during any given year. If a person has 6 household appliances, what is the probability that exactly 2 of them will fail next year?
(x) npq =
P(.6+.94)=1 6*2=12
To find the probability of exactly 2 appliances failing next year, we can use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * q^(n-x)
Where:
- P(x) is the probability of x events occurring,
- n is the total number of trials (6 appliances in this case),
- x is the number of successful events (2 appliances failing in this case),
- p is the probability of success (the probability of an appliance failing, which is 6% or 0.06),
- q is the probability of failure (1 - p or 0.94), and
- (nCx) is the number of combinations of n things taken x at a time.
Calculating this specific probability:
P(2) = (6C2) * (0.06^2) * (0.94^(6-2))
First, calculate (6C2):
6C2 = (6!)/(2!*(6-2)!)
= (6*5)/(2*1)
= 15
Next, substitute the values into the formula:
P(2) = (15) * (0.06^2) * (0.94^4)
= 0.225216
So, the probability that exactly 2 out of 6 household appliances will fail next year is approximately 0.225216, which is approximately 22.52%.