Question bank: Binomial Probability

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Question 1:

Hard

A shooter is participating in a target shooting competition. He has a 70% probability of hitting the target in a single shot. However, the competition consists of 10 rounds of shots, and the shooter wants to calculate the probability of hitting exactly 7 shots. Considering that each round is independent and that the probability of hitting or missing the target does not change throughout the competition, calculate the binomial probability of the shooter hitting 7 shots in 10 rounds. Consider using the binomial distribution formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)), where n is the number of trials, k is the desired number of successes, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient, which can be calculated as n! / (k! * (n-k)!). After the calculations, discuss how the probability of hitting 7 shots in 10 rounds compares to the probability of hitting 5 or 6 shots, and which factors influence these probabilities.

Binomial Probability

Contextualized Question

Calculus Question

Question 2:

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 3:

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 4:

Hard

A class of students is preparing for the Physics test and one of them, Pedro, claims to have an accuracy rate of 60% in each question he answers. The Physics exam has a total of 10 questions. What is the probability of Pedro getting exactly 7 questions right?

Binomial Probability

Question 5:

Medium

In a target shooting competition, a shooter has an 80% chance of hitting the target with each shot. He must take 5 consecutive shots and will be awarded based on the number of hits. a) What is the probability of him hitting exactly 3 out of the 5 shots? b) What is the probability of him hitting at least 4 out of the 5 shots? c) If he decided to shoot only 3 times, what would be the probability of hitting all targets?

Binomial Probability

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