Question

Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 4.

Answer 1

Answer:

$Probability = \frac{1}{36}$

Step-by-step explanation:

Given

Two fair dice

Required

Determine the probability that the outcomes is 6 on the first and 4 on the second

First, we need to write out the sample space of both:

$S_1 = \{1,2,3,4,5,6\}$

$n(S_1) = 6$

$S_2 = \{1,2,3,4,5,6\}$

$n(S_2) = 6$

Where S1 represents the first and S2, the second

The probability of outcome of 6 on the first is:

$P(6) = \frac{n(6)}{n(S_1)}$

$P(6) = \frac{1}{6}$

The probability of outcome of 4 on the second is:

$P(4) = \frac{n(4)}{n(S_2)}$

$P(4) = \frac{1}{6}$

So, the required probability is then calculated as:

$Probability = P(6) * P(4)$

$Probability = \frac{1}{6} *\frac{1}{6}$

$Probability = \frac{1}{36}$