Question

If you roll a fair die 3 times, what is the probability that all 3 rolls will come up a value less than 4?

Answer 1

Getting a value less than 4 means either 1, 2 or 3. (and not 4, 5 or 6) So, there are 3 favourable outcomes out of 6 total outcomes (for a single roll)

Probability of getting a value less than 4 in 1st roll = 3/6 = 1/2

Probability of getting a value less than 4 in 2nd roll = 3/6 = 1/2

Probability of getting a value less than 4 in 3rd roll = 3/6 = 1/2

These are 3 independent events, so we can multiply the probabilities.

So, total probability of getting a value less than 4 in all the 3 rolls = (!/2) * (!/2) * (!/2) = 1/8 = 0.125

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