Question

John rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 7, given that the first roll is a 1?
one over six
one over three
one over two
five over six

Answer 1

Answer:  The correct option is (d) five over six.

Step-by-step explanation:  Given that John 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 1.

The sample space of an event of rolling a cube is

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

That is, n(S) = 6.

Now, let 'A' be the event that the sum of the two rolls is less than 7, then

A = {1, 2, 3, 4, 5}.

That is, n(A) = 5.

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

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{5}{6}.$

Thus, the required probability is five over six.

Option (d) is correct.

Answer 2

The probability would be 5/6.

There are 6 ways we can roll two dice and have the first number be a 1:
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6

Out of these, 5 possibilities give us a sum less than 7:
1, 1
1, 2
1, 3
1, 4
1, 5

Thus we have 5/6.