Question

Five cards are selected at random without replacement from a standard
deck of 52 cards. The order of the selection is not considered.
Let S be the sample space connected to this experiment.
Let R be the event that all of the cards selected are red.
Let W be the event that none of the cards selected are hearts
a) Find n(S)

b) Find P(R)

c) Find P(W)

d) Find P(R|W)

e) Are the events R and W independent? Justify your response.

Answer 1

a)n(S)=⁵²C₅ =52!/(5!*(52-5)!) =2598960

b)P(R)=P(all cards are red)=P(sleecting all 5 cards from 26 of red cards)=²⁶C₅/⁵²C₅

=65780/2598960=3289/129948=0.025310

c)

P(W)=P(all 5 are non hearts cards)=P(selecting all 5 from remaining 39 cards)=

=575757/2598960=0.221534

d)P(W n R) =P(all 5 are red and no hearts)=P(all 5 are diamond cards)=

=1287/2598960=0.000495

P(R|W)=P(R n W)/P(W) =0.000495/0.221534=0.002234

e)

as P(R|W) is not equal to P(R) ; threfore R and W are not independent,