Question

In: Statistics and Probability

When you have two dice rolling at the same time, find the following probabilities with proper...

When you have two dice rolling at the same time, find the following probabilities with proper explanations.

(1) When you will observe a total of 8

(2) When you will observe a total of 4 or a total of 6

(3) When you will observe at least a total of 2

Solutions

Expert Solution

Two dice are rolled at the same time.

So,the first dice can show 6 results and for each of them , the second can also show 6 results.

So,there are a possible 6*6=36 cases.

(1) Probability that a total of 8 is observed.

This can be achieved by the results

(2,6),(3,5),(4,4),(5,3),(6,2).

So,there are 5 favourable cases where we observe a total of 8.

So,required Probability

=5/36

(2) Probability that a total of 4 or a total of 6 is observed.

A Total of 4 is observed in the following cases

(1,3),(2,2),(3,1).

A Total pf 6 is observed in following cases

(1,5),(2,4),(3,3),(4,2),(5,1).

So

P(Total of 4 or total of 6)

=P(total of 4) +P(total of 6)

=3/36+5/36

=8/36

=2/9.

(3) Probability that at least a total of 2 is observed

=1-P(total less than 2)

Now,the minimum number that the dice show is 1,so the minimum total of them is 2.

So the probability that the P(total less than 2) is 0.

So,our required Probability is 1.

orchestra answered 2 years ago
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