Question

A standard deck of cards contains 52 cards. One card is selected from the deck.

(a) Compute the probability of randomly selecting a diamond or club.
(b) Compute the probability of randomly selecting a diamond or club or heart.
(c) Compute the probability of randomly selecting a five or club.

Answer 1

1) Probability of randomly selecting a diamond or club =
`(1)/(2)`

2)Probability of randomly selecting a diamond or club or heart =
`(3)/(4)`

3) P(selecting a five or club) =
`(4)/(13)`

Explanation:

Total cards in the deck = 52

Noe Let E : favorable Event

So,
`P(E) =  \frac{\textrm{Number of Favorable outcomes}}{\textrm{Total outcomes}}`

1 ) Probability of randomly selecting a diamond or club

Here the favorable event is picking a club or diamond

hence, favorable outcomes = Number of club and diamond

= 13 + 13 = 26

⇒P(selecting a diamond or club) =
`(26)/(52)  = (1)/(2)`

2) Probability of randomly selecting a diamond or club or heart

Here the favorable event is picking a diamond and club and heart.

hence, favorable outcomes = Number of clubs + diamond + heart

= 13 + 13 + 13 = 39

⇒P(selecting a diamond or club or heart) =
`(39)/(52)  = (3)/(4)`

3 )Probability of randomly selecting a five or club.

Here the favorable event is selecting a five or club.

hence, favorable outcomes = Number of 5 in a deck + Number of clubs

= 3 + 13 = 16

⇒P(selecting a five or club) =
`(16)/(52)  = (4)/(13)`