A box contains three blue cards and two yellow cards. Suppose that Arahia choose

Question

A box contains three blue cards and two yellow cards. Suppose that Arahia chooses a card and then Bin chooses a card from the four cards remaining in the box. (Note: to gain full marks you must define events and express the required probabilities in terms of these events as well as giving the correct numerical answer ) (a) What is the probability that Arahia chooses a blue card. (b) If Arahia chooses a blue card, what is the probability that Bin chooses a yellow card? (c) If Arahia chooses a yellow card, what is the probability that Bin also chooses a yellow card? (d) What is the probability that both Arahia and Bin choose a blue card? (e) What is the probability that Bin chooses a yellow card? (f) If Bin chooses yellow card what is the probability that Arahia chose a blue card?

Explanation / Answer

a) Probability that Arahia chooses a blue card = 3/5 =0.6

b) Probability that Bin chooses a yellow card, given Arahia chose blue card = 2/4 = 0.5

c) Probability that Bin chooses a yellow card, given Arahia chose yellow card too = 1/4 =0.25

d) Probability that both chose blue card = 3C2/ 5C2 = 3/10

e) Probability that bin chose yellow card = 2/5 = 0.4

f) Probability that Arahia chose a blue card, given bin chose yellow card = 3/4 =0.75

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