Answer:
P(A) = 31/1296
P(B) = 125/1296
Step-by-step explanation:
Here, we want to find P(A) and P(B)
Let’s start with A
In a roll of a die, the probability that there will be a 5 is 1/6
The probability of not having a 5 is therefore 1-1/6 = 5/6
So out of four rolls , we want to find the probability of having at least two fives
This means there could be 2, 3 or 4 fives;
For two fives;
We have 2 fives and two non-fives
= (1/6 * 1/6 * 5/6 * 5/6) = 25/1296
For 3 fives;
we have 3 fives and 1 non five
= 1/6 * 1/6 * 1/6 * 5/6 = 5/1296
For 4 fives;
= 1/6 * 1/6 * 1/6 * 1/6 = 1/1296
So the probability of at least two fives is;
1/1296 + 5/1296 + 25/1296 = 31/1296
Event B is the probability that there is at most one five among the four rolls
That means there are 3 non fives and 1 five
P(B) = 1/6 * 5/6 * 5/6 * 5/6 = 125/1296
