Practice Binomial Distribution – Complete Detail (18.X) - Binomial Distribution

Practice: Binomial Distribution – Complete Detail

Lesson 18.XBinomial Distribution

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11 questions

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6 sample questions

Question 1.
What is the probability of getting exactly 1 head when you flip a fair coin twice?
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Use the PMF formula for n=2, k=1, and p=0.5.
Question 2.
If a die is rolled 3 times, what is the probability of getting exactly 2 sixes?
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Recognize there are 3 ways to choose which roll is not a six.
3Question 3.
What is the formula for the probability mass function of the Binomial Distribution?
- P(X = k) = (n choose k) * p^(n-k) * (1-p)^k
- P(X = k) = (n-k choose k) * p^k * (1-p)^n
- P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
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Remember the arrangement of p and (1-p) with respect to k and n.
4Question 4.
The mean of a binomial distribution is calculated as which of the following?
- E(X) = n(1 - p)
- E(X) = np
- E(X) = p/n
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Think about how the average number of successes is determined.
Question 5.
A biased coin shows a 60% chance of landing heads. If flipped 10 times, what is the probability of getting exactly 6 heads?
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Calculate the binomial coefficient and powers separately.
Question 6.
In a shipment of 100 items, 90% are defect-free. If 15 items are chosen at random, compute the probability that at least 12 will be defect-free.
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Consider using a cumulative approach for summation.

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