Question

PLEASE HELP EASY A fair number cube is rolled twice. Determine whether each event is more or less likely than rolling the same number both times.

Select the correct button in the table to show the likelihood of each event.

Answer 1

Explanation:

a probability is always the ratio

desired cases / totally possible cases

the probably for the second roll to roll the same number as in the first roll again, is actually pretty high.

it means that we "accept" any result in the first roll. that makes this a 6/6 = 1 probability.

and then for the second roll we have the usual 1/6 probability (to roll the same number again).

so, we have

6/6 × 1/6 = 1/6 = 0.166666666...

P(even, odd) is the probability to roll first an even number (3 out of 6 = 3/6 = 1/2) and then an odd number (again 3 out of 6 = 1/2) :

1/2 × 1/2 = 1/4 = 0.25

so, this is more likely.

P(2, 5) is the probability to roll first a 2 (1 out of 6 is 1/6) and then a 5 (again 1 out of 6 is 1/6) :

1/6 × 1/6 = 1/36 = 0.027777777...

so, this is less likely.

P(odd, 1) is the probability to roll first an odd number (3 out of 6 = 1/2) and then a 1 (1 out of 6 = 1/6) :

1/2 × 1/6 = 1/12 = 0.083333333...

so, it is less likely.