7th grade math probability

Question

Drew rolls 2 number cubes 75 times. Is it likely that she will get a sum of 3 more than 5 times? Explain

Answer 1

With two number cubes, there are 36 possible rolls - 6 * 6 = 36 (6 possible rolls with each die). 2 rolls get you a 3, 1, 2 and 2,1. Thus, the probability of a 3 on each roll is 2/36 = 1/18

Thus, in 75 rolls, you would expect to roll a 3 1/18 * 75 = 4 1/6 times. You would then expect more than 5 rolls of 3 less than half the time.

You can actually work out the exact probabilities in Excel using the binomial distribution.

P(more than 5 rolls of 3) = 1 - binom.dist(5,75,1/18,1) = 0.237463327411833

An internet search will be teach you about the binomial distribution and the formula in Excel.