Question

What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number.

Answer 1

Question:

Carl throws a single die twice in a row. For the first throw, Carl rolled a 2; for the second throw he rolled a 4. What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number. O 22% 36% O 3% O 33%

Answer:

The probability of rolling a 2 then 4 is 3%

Step-by-step explanation:

Given

A die rolled twice

Required

Probability of rolling a 2 then 4; i.e. P(2 n 4)

First, we need to list out the sample space

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

$n(S) = 6$

Next, is to calculate P(2)

$P(2) = \frac{n(2)}{n(S)}$

$P(2) = \frac{1}{6}$

Next, is to calculate P(4)

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

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

Next,is to calculate the required probability using the following formula

$P(2\ n\ 4) = P(2) * P(4)$

$P(2\ n\ 4) = \frac{1}{6} * \frac{1}{6}$

$P(2\ n\ 4) = \frac{1}{36}$

$P(2\ n\ 4) = 0.02777777777$

Convert to Percentage

$P(2\ n\ 4) = 2.777777777\%$

Approximate

$P(2\ n\ 4) = 3\%$

Hence, the probability of rolling a 2 then 4 is 3%