Question

Roll a pair of dice. Are the events of getting a sum of 10 OR rolling two of the same number mutually exclusive? What is the probability of getting either

Answer 1

B. not mutually exclusive, 2/9

EXPLANATION :

From the problem, we have a pair of dice, and the total events in rolling a pair of dice is 6 x 6 = 36

We have two event that are needed to consider.

One event is getting a sum of 10

and the other event is rolling two of the same number.

Mutually exclusive events are events that can be happened simultaneously. It means that the events are different.

For the first event, we need a sum of 10, that will be 4 and 6, 5 and 5, then 6 and 4. A total of 3 events.

For the second event, we need two of the same number, that will be 1 and 1, 2 and 2, 3 and 3, 4 and 4, 5 and 5, then 6 and 6. A total of 6 events.

Take note that between these two events, there is one common event which is 5 and 5.

So this is NOT Mutually Exclusive

Getting the probability :

(Probability of first event) + (Probability of second event) - (probability of common event)

Probability of first event will be 3/36

Probability of second event will be 6/36

Probability of common event will be 1/36

`(3)/(36)+(6)/(36)-(1)/(36)=(8)/(36)\quad or\quad (2)/(9)`

The probability is 2/9