Answer to Question #103506 in Statistics and Probability for Josh

Question

Which of the following are mutually exclusive outcomes from rolling a pair of dice?
A. The total number of pips of the upper faces of the dice is 5 and there are five pips on one die.
B. A total number of pips is 7 and both die has odd number of pips

Answer 1

Two events are mutually exclusive if they cannot occur at the same time.

A six-sided die is a cube with a different number of pips on each face (side), ranging from 1 to 6.

Two events E and F are mutually exclusive if the intersection of E and F is empty.

A pair of dice is rolled.

A.

The event E= "the total number of pips of the upper faces of the dice is 5" has possible outcomes:

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

The event F= "there are five pips on one die when in rolling a pair of dice is rolled " has possible outcomes:

$(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5),$

$(5, 1), (5, 2), (5, 3), (5, 4), (5, 6)$

E and F have no elements in common and therefore are mutually exclusive.

B.

The event E= "the total number of pips is 7" has possible outcomes:

$(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)$

The event F= " both die has odd number of pips" has possible outcomes:

$(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)$

E and F have no elements in common and therefore are mutually exclusive.