Question

Two number cubes are rolled for two separate events:

Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Find the conditional probability of B given that A occurs first.

Enter your answer as a simplified fraction.

Answer 1

Using it's concept, it is found that the conditional probability of B given that A occurs first is of $p = \frac{3}{10}$.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

When two dice are rolled, we have these 36 outcomes:

• (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)

Of those, 30 involve a sum of less than 10, and of those 30, 9 involve a sum that is multiple of 3(either 3, 6 or 9), hence the probability is given by:

$p = \frac{9}{30} = \frac{3}{10} = 0.3$

More can be learned about probabilities at https://brainly.com/question/14398287

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