You are rolling a number cube two times. what is the probability of rolling an odd number on the first roll and then a number greater than 4 on the second roll?

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01-09-2022
Mathematics

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You are rolling a number cube two times. what is the probability of rolling an odd number on the first roll and then a number greater than 4 on the second roll?

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Anshuyadav Anshuyadav · Answer 1 · 2022-09-07T13:51:27-04:00

The probability of rolling an odd number on the first roll and then a number greater than 4 on the second roll is 1/6.

According to the given question.

A cube is rolled two times.

So, the sample space for rolling a cube is given by

S = {(1, 1), (1, 2), (1, 3),(1, 4), (1, 5),(1, 6), (2,1), (2, 2), (2, 3), (2,4), (2, 5), (2, 6),(3, 1)(3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Total number of coutcomes = 36

The possible outcomes for rolling an odd number on the first roll and then a number greater than 4 on the second roll = {(1, 5), (1, 6), (3, 5), (3, 6), (5, 5), (5, 6)}

⇒ Total number of favorable outcomes = 6

Thereofore,

The probability rolling an odd number on the first roll and then a number greater than 4 on the second roll

= 6/36

= 1/6

Hence, the probbaility rolling an odd number on the first roll and then a number greater than 4 on the second roll is 1/6.

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