Question

you draw a single card from a standard 52-card deck. find the probability of each event. simplify the probability ratio or write in decimal form. a) ace or a nine b) not a king c) club or a face card d) spade or a heart e) neither a diamond nor a 7

Answer 1

Solution:

total number of cards in a deck = 52

( a )

number of aces in a deck = 4

number of nines in a deck = 4

probability of selecting an ace or a nine = ( 4 + 4 ) / 52 = 8 / 52 = 0.1538

( b )

number of kings in a deck = 4

probability of selecting a king = 4 / 52 = 0.0769

probability of not selecting a king = 1 - ( probability of selecting a king )

= 1 - ( 0.0769 )

= 0.9230

( c )

number of club cards in a deck = 13

number of face cards in a deck = 4 * 4 = 16

number of face cards in club cards = 4

probability of selecting a club or a face card = ( 13+16-4 ) / 52 = 25 / 52

= 0.4807

( d )

number of spades in a deck = 13

number of hearts in a deck = 13

probability of selecting a spade or a heart = ( 13 + 13 ) / 52 = 0.5000

( e )

number of diamonds in a deck = 13

number of sevens in a deck = 4

number of seven of diamonds in a deck = 1

probability of selecting a diamond or a seven = (13+4-1) / 52 = 16 / 52 = 0.3076

probability of selecting nor a diamond nor a seven = 1 - ( (13+4-1) / 52 ) = 1 - (16 / 52 )

= 1-  0.3076

= 0.6923