Question

Determine if the following is mutually exclusive (Disjoint) or overlapping and then calculate the probability. A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a 10 or a spade?

Answer 1

`(4)/(13)`

Explanation:

GIVEN: Determine if the following is mutually exclusive (Disjoint) or overlapping and then calculate the probability. A card is randomly selected from a standard deck of
`52` playing cards.

TO FIND: What is the probability that it is a
`10` or a spade.

SOLUTION:

getting a
`10` and getting a spade are not disjoint events as both can occur simultaneously.

Now probability of getting a spade
`P(A)=\frac{\text{total spade cards}}{\text{total cards in deck}}`

`=(13)/(52)=(1)/(4)`

probability of getting a
`10`
`P(B)=\frac{\text{total cards of 10}}{\text{total cards}}`

`=(4)/(52)=(1)/(13)`

probability of getting a
`10` and a spade
`P(A\cap B)=\frac{\text{total cards of spade that are 10}}{\text{total cards}}`

`=(1)/(52)`

probability of getting a
`10` or a spade
`=P(A)+P(B)-P(A\cap B)`

`=(1)/(4)+(1)/(13)-(1)/(52)`

`=(4)/(13)`

probability that it is a 10 or a spade is
`(4)/(13)`