Question

Question No. 1
A pair of dice is rolled. Find P(A/B) if the events A and B are
A: 2 appears on at least one dice
B: sum of the numbers appearing on dice is 6​

Answer 1

Answer:

Let us name the two dice M and N

The number on each die can take the values 1, 2, 3, 4, 5 and 6.

Let us here define the ordered pair (x,y) where x denotes the number appearing on die M and y denotes the number appearing on die N.

In the given condition at least one of x and y has to be 2, and the other has taken any value from 1 to 6. We need to find in how many cases x+y = 6

So, the sample space (more technically the reduced sample space with respect to the experiment) is

A=(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)

It has 11 elements. So we can write n(A)=11.

Now our event is getting a sum = 6, when one of the die shows 2.

We can define this event as B, =(2,4),(4,2)

Clearly, n(B)=2

In simple words, out of 11 possible outcomes 2 outcomes are favourable.

Hence the probability of event A and B, which is nothing but the probability that the sum of the numbers on the two dice is 6 if 2 appear on at least one of the dice when two dice are thrown, is given by

P(A/B)=n(B)/n(A)=2/11.

Therefore the probability that you require is 2/11≈0.181

Answer 2

I hope it's correct and it will help you....☺️