Question

Toss 3 dice. What's the probability that a 4 will come up exactly twice?

Answer 1

Answer:

$\bold{\dfrac{1}{12}}$

Step-by-step explanation:

The dice is rolled 3 times.

To find:

The probability that a 4 will come up exactly twice = ?

Solution:

Let 4 comes up exactly twice, let the third number be $x$.

The possible outcomes can be:

($x$, 4, 4) where $x$ can be any number between 1 to 6 , so 6 outcomes.

(4, $x$, 4) where $x$ can be any number between 1 to 6 , so 6 outcomes.

(4, 4, $x$) where $x$ can be any number between 1 to 6 , so 6 outcomes.

So, the total number of favorable outcomes possible = 6 + 6 + 6 = 18

Total number of outcomes that can be possible at roll of 3 dice:

6 $\times$ 6 $\times$ 6  = 216

Formula for probability of an event E is given as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(\text{exact 2 fours}) = \dfrac{18}{216}\\\Rightarrow \bold{P(\text{exact 2 fours}) = \dfrac{1}{12}}$