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Question bank: Binomial Probability

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Question 1:

Medium

A factory produces screws, and its quality control team has verified that the probability of a screw being defective is 4%. The factory packs packages with 10 screws each. What is the probability of a randomly selected package containing exactly 2 defective screws?
Binomial Probability
Question 2:

Easy

In an archery competition, an archer has a 70% probability of hitting a target in each of his attempts. He has the opportunity to make 5 shots. Considering that each shot is independent and the probability of hitting remains constant in all attempts, calculate the probability of the archer hitting exactly 3 shots on target. Use the binomial distribution to solve the question.
Binomial Probability
Question 3:

Medium

During a training session, an archer needs to hit a target with 60% accuracy. She shoots a total of 10 arrows, and her coach wants to know the chances of her hitting the target at different moments. (a) What is the probability of the archer hitting exactly 4 out of the 10 arrows on the target? (b) What is the probability of the archer hitting at least 7 out of the 10 arrows on the target? (c) What is the probability of the archer hitting between 5 and 8 arrows on the target, inclusive?
Binomial Probability
Question 4:

Medium

During an archery competition, an archer has a 60% chance of hitting the target on each attempt. Only five arrows are available for each participant.
Binomial Probability
Question 5:

Medium

On a farm, laying hens have a 70% probability of laying an egg every day. A farmer collects the eggs from 10 hens for three consecutive days and wants to know the probability of obtaining a specific number of eggs. Contextualize the situation and answer the following items: (a) Determine the probability of the farmer collecting 8 eggs on the first day. (b) Calculate the probability of the farmer collecting a total of 22 eggs over the three days. (c) Find and justify which day would have the highest probability of obtaining the greatest number of eggs.
Binomial Probability
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