Binomial Probability Distributions

5 Questions | By Dana Deuitch | Updated: May 23, 2018 | Attempts: 151

Some mathematical problems for students are harder to comprehend than others. Probability is the measure of the likelihood that an event will occur. Binomial probability however measures just two outcomes, either success or failure. Work on the questions provided to polish up on your knowledge of this technique. All the best!

Questions and Answers

1.

A bag contains 100 marbles of which 20 are yellow and 80 are blue. The bag is shaken, a marble is drawn, its color recorded, then returned to the bag and the bag is shaken again. This process is repeated sixty-nine more times. What is the probability that exactly 55 of the marbles selected were blue? (Round your answer to 2 decimal places).

Explanation
Indpendent trials (probabilities don't change since we return the marbles) = Binomial distribution
70C55 * (0.8)^55 * (0.2)^15 = 0.11

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2.

A single die is rolled four times. What is the probability of rolling a 6 exactly twice?(Round your answer to 2 decimal places).

Explanation
Independent trials (probability of rolling a 6 does not change) = Binomial distribution
4C2 * (1/6)^2 * (5/6)^2

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3.

A single die is rolled four times. What is the probability of rolling a 6 at least twice?(Round your answer to 2 decimal places).

Explanation
Independent trials (probability of rolling a 6 does not change) = Binomial distribution
P(at least twice) = P(2) + P(3) + P(4)
P(2) = 4C2 * (1/6)^2 * (5/6)^2

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4.

A bag contains 100 marbles of which 20 are yellow and 80 are blue. The bag is shaken, a marble is drawn, its color recorded, then returned to the bag and the bag is shaken again. This process is repeated ninety-nine more times. What is the probability that between 85 and 87 of the marbles selected were blue? (Round your answer to 2 decimal places).

Explanation
Indpendent trials (probabilities don't change since we return the marbles) = Binomial distribution
P(85) + P(86) + P(87)
P(85) = 100C85 * (0.8)^85 * (0.2)^15 = 0.048

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5.

Given that 3% of all Mars Bars made at the Newmarket Mars factory are less than the weight on the package, if 30000 chocolate bars are produced on any given day, how many would be expected to be below weight?(Round your answer to 2 decimal places).

Explanation
would be expected => Expected Value
how many below weight => p = probability that one is below weight = 3% = 0.03
30000 produced => n=30000
E(x) = np

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