Question

Jack rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 8 given that the first roll is a 4?

one over two

one over six

one over three

five over six

Answer 1

Answer: The correct option is (a) one over two.

Step-by-step explanation: Given that Jack rolls a number cube twice. We are to find the probability that the sum of the 2 rolls is less than 8 given that he first roll is a 4.

A cube rolls 1, 2, 3, 4, 5 and 6. So, the sample space will be

S = {1, 2, 3, 4, 5, 6}.

That is, n(S) = 6.

Since the first roll is a 4, so the options for the second roll are 1, 2 and 3 so that the sum is less than 8.

Therefore, if 'A' is the event that the sum is less than 4, then

A = {1, 2, 3}.

That is, n(A) = 3.

So, the probability of happening of event A is given by

`P(A)=(n(A))/(n(S))=(3)/(6)=(1)/(2).`

Thus, the required probability is one over half.

Option (a) is correct.

Answer 2

If the first roll is a 4, the possibilities to add less than 8 are that the second cube roll is 1, 2 or 3.

These are 3 different events out of 6 possilbe ones, which is 3 / 6 = 1 / 2; i.e. half of times.

Then the answer is the first option: 1 / 2