A child mixes ten good and three dead batteries. To find the dead batteries, his father tests them one by one and without replacement. What is the probability that his father finds all three dead batteries at the fifth test?

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Answer 1 · 2017-02-10T10:20:42

See explanation.

If you use the binomial scheme the parameters would be:

Success event: "finding a dead battery"
Failure event: "finding a good battery"

Success probability: #p=3/13#

Failure probability #q=1-p=10/13#

The number of tries #n=5#
Expected number of successes #k=3#

Now we have all data needed to calculate the probability:

#P(k=3)=(""_3^5)xx(3/13)^3xx(10/13)^2=#

#=(5!)/(3!xx2!)xx(3/13)^3xx(10/13)^2=#

#=(4xx5)/2xx(27xx100)/13^5=#

#=27000/13^5=27000/371293~~0.073#

Answer: The chance of finding all dead batteries in 5 tries is #0.073#

A child mixes ten good and three dead batteries. To find the dead batteries, his father tests them one by one and without replacement. What is the probability that his father finds all three dead batteries at the fifth test?