Question

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

Answer 1

Answer:

1) Probability of randomly selecting a diamond or club = $\frac{1}{2}$

2)Probability of randomly selecting a diamond or club or heart = $\frac{3}{4}$

3) P(selecting a five or club) = $\frac{4}{13}$

Step-by-step 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) = $\frac{26}{52} = \frac{1}{2}$

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) = $\frac{39}{52} = \frac{3}{4}$

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) = $\frac{16}{52} = \frac{4}{13}$