1.An experiment is performed where a person draws a card from a regular 52 card

Question

1.An experiment is performed where a person draws a card from a regular 52 card deck. If the card is a heart then they flip a fair coin once if the card is a spade, club or diamond they flip a fair coin twice. Calculate the following probabilities.

a.What is the probability that exactly one head is flipped in the experiment?

b.What is the probability that one head and one tail is flipped?

c.If exactly one head is flipped in the experiment what is the probability that a heart was drawn?

d.If at least one tail is flipped in the experiment what is the probability that a spade was drawn?

Explanation / Answer

a)probability that exactly one head is flipped in the experiment=(1/4)*(1/2) +(3/4)[2*(1/2)*(1/2)] =1/2= 0.5

b)probability that one head and one tail is flipped=(3/4)[2*(1/2)*(1/2)] =0.375

c) probability that a heart was drawn .If exactly one head is flipped in the experiment=

{(1/4)*(1/2)} /{(1/4)*(1/2) +(3/4)[2*(1/2)*(1/2)} =0.125/0.5 = 0.25

d)Probality for atleast on tail =(1/4)*(1/2) +(3/4)[1-(1/2)*(1/2)] =0.6785

Probality for atleast on tail and spade was drawn =(1/4)*[1-(1/2)*(1/2)] =0.1875

so probability that a spade was drawn If at least one tail is flipped in the experiment = 0.1875/0.6785 =0.2763

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