A bag contains blue pens and black pens. Every time a pen is randomly taken from the bag, a pen of the same color is replaced. Forty percent of the pens are blue.

Part A: What is the probability, rounded to the nearest thousandth, of picking at least 3 black pens when taking 5 pens from the bag?

Question

28-01-2025
Mathematics

High School

Welcome to the article A bag contains blue pens and black pens Every time a pen is randomly taken from the bag a pen of the same color is. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

A bag contains blue pens and black pens. Every time a pen is randomly taken from the bag, a pen of the same color is replaced. Forty percent of the pens are blue.

Part A: What is the probability, rounded to the nearest thousandth, of picking at least 3 black pens when taking 5 pens from the bag?

Answer :

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puneetknp721 puneetknp721 · Answer 1 · 2025-03-01T08:57:16-05:00

Final answer:

The probability of drawing at least 3 black pens from a bag, where 60% of the pens are black and pens are replaced after each draw, can be found using the binomial probability formula.

Explanation:

The question asks for the probability of picking at least 3 black pens from a bag containing 40% blue pens (and thus 60% black pens) upon drawing 5 pens, with the same color pen being replaced each time.

This problem can be solved using the binomial probability formula, which states that the probability of having exactly k successes (in this case, drawing a black pen) in n trials (drawing pens) is given by P(X= k) = (nCk) (p^k) ((1-p)^(n-k)), where n is the total number of trials, k is the number of successful trials, p is the probability of success on each trial, and nCk is the combination of n items taken k at a time.

Since we are interested in the probability of picking at least 3 black pens, we need to calculate the probability for 3, 4, and 5 black pens being drawn and then sum these probabilities. With p=0.60 (since 60% of the pens are black) and n=5, the calculations would involve using the binomial formula for k=3, k=4, and k=5, and then adding these probabilities together for the final answer.

A bag contains blue pens and black pens. Every time a pen is randomly taken from the bag, a pen of the same color is replaced. Forty percent of the pens are blue.Part A: What is the probability, rounded to the nearest thousandth, of picking at least 3 black pens when taking 5 pens from the bag?

Answer :

Final answer:

Explanation:

Other Questions

A bag contains blue pens and black pens. Every time a pen is randomly taken from the bag, a pen of the same color is replaced. Forty percent of the pens are blue.

Part A: What is the probability, rounded to the nearest thousandth, of picking at least 3 black pens when taking 5 pens from the bag?