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There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.
Step-by-step explanation:
With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:
- n=4 (the amount of batteries picked for the sample).
- p=3/10=0.3 (the proportion of dead batteries).
- k≥1 (the amount of dead batteries in the sample needed to not sell the package).
The probability of having k dead batteries in the sample is:
Then, the probability of having one or more dead batteries in the sample (k≥1) is: