Answer:
![\bold{\dfrac{1}{12}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cdfrac%7B1%7D%7B12%7D%7D)
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
.
The possible outcomes can be:
(
, 4, 4) where
can be any number between 1 to 6 , so 6 outcomes.
(4,
, 4) where
can be any number between 1 to 6 , so 6 outcomes.
(4, 4,
) where
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
6
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}}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20cases%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20cases%7D%7D)
![P(\text{exact 2 fours}) = \dfrac{18}{216}\\\Rightarrow \bold{P(\text{exact 2 fours}) = \dfrac{1}{12}}](https://tex.z-dn.net/?f=P%28%5Ctext%7Bexact%202%20fours%7D%29%20%3D%20%5Cdfrac%7B18%7D%7B216%7D%5C%5C%5CRightarrow%20%5Cbold%7BP%28%5Ctext%7Bexact%202%20fours%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B12%7D%7D)