Question

5) [2] Find answers as fractions (no decimals). Show work when possible for full credit. Given a standard deck of 52 playing cards, a) if you draw one card at random, what is the probability it is a diamond or a club?

b) if you draw one card at random, what is the probability it is a two, three, or a spade?

c) if you draw two cards at random, what is the probability of drawing a Jack and then a heart, with replacement?

d) if you draw two cards at random, what is the probability of drawing a heart and then a spade, without replacement?

Answer 1

a) P( Diamond or club) = P( diamond) + P( club) - P( diamond and club)

= (13/52) + (13/52) - 0

= 1/2

b) P( two, three or spade)

= P( Two) + P( Three) + P( Spade) - P( two and three) - P( two and spade) - P( three and spade) + P( two and three and spade)

= (4/52) + (4/52) + (13/52) - 0 - (1/52) - (1/52) +0

= 19/52

c) P( Jack and heart with replacement) = P( jack ) * P( heart)

= (4/52) * ( 13/52)

= 1/52

d) P( heart and then a spade without replacement)= P( heart) * P( spade)

= (13/52) * (13/51)

= 13/204