## Related questions with answers

Two events are said to be mutually exclusive (or disjoint) if it is impossible for both of them to occur on the same outcome. Which of the following pairs of events are mutually exclusive? a. You roll a sum of 7 with a pair of dice; you get doubles on the same roll. b. You roll a sum of 8 with a pair of dice; you get doubles on the same roll. c. Isaac wears white shoes today to class; Isaac wears black shoes today to class. d. Yen owns white shoes; Yen owns black shoes. e. Pat is a boy, Pat said most students in his school are friendly. f. Bernardo said that all students are friendly; Bernardo said most students are friendly.

Solution

Verified(a) Two events are $\textbf{disjoint}$ or $\textbf{mutually exclusive}$, if the events cannot occur at the same time.

It is not possible to roll a sum of 7 while also rolling doubles, as a sum of 7 can only be obtained by rolling (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) non of which are doubles, and thus the events of rolling a 7 and getting doubles are $\textbf{mutually exclusive}$.

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