Binomial Probability:

Question

If a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 2 fours?

Answer 1

Binomial probability with:

n = 5 trials (rolls of the die)

"success" = getting a 4 when the die is rolled once

probability of "success": p = 1/6

Binomial random variable:

X = total number of "successes" in 5 trials

Possible values: X = 0, 1, 2, 3, 4, 5

You need P(X ≥ 2) = ?

Any Binomial calculator will do.

If you need to calculate it manually, you have to sum up the following probabilities:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

or the equivalent shorter calculation:

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)

because the sum of all outcomes gives you a total probability of 1.

Answer 2

I have worked this problem out in this video for you. Check it out and let me know if you have any additional question. Take care!

Dr. Christal-Joy Turner