Respuesta :
Answer:
[tex]\frac{4}{13}[/tex]
Step-by-step 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 [tex]52[/tex] playing cards.
TO FIND: What is the probability that it is a [tex]10[/tex] or a spade.
SOLUTION:
getting a [tex]10[/tex] and getting a spade are not disjoint events as both can occur simultaneously.
Now probability of getting a spade [tex]P(A)=\frac{\text{total spade cards}}{\text{total cards in deck}}[/tex]
[tex]=\frac{13}{52}=\frac{1}{4}[/tex]
probability of getting a [tex]10[/tex] [tex]P(B)=\frac{\text{total cards of 10}}{\text{total cards}}[/tex]
[tex]=\frac{4}{52}=\frac{1}{13}[/tex]
probability of getting a [tex]10[/tex] and a spade [tex]P(A\cap B)=\frac{\text{total cards of spade that are 10}}{\text{total cards}}[/tex]
[tex]=\frac{1}{52}[/tex]
probability of getting a [tex]10[/tex] or a spade[tex]=P(A)+P(B)-P(A\cap B)[/tex]
[tex]=\frac{1}{4}+\frac{1}{13}-\frac{1}{52}[/tex]
[tex]=\frac{4}{13}[/tex]
probability that it is a 10 or a spade is [tex]\frac{4}{13}[/tex]
