Four cards (without replay) are drawn from a well-mixed deck of cards (with 52 cards). What is the probability of getting (a) exactly two aces (b) at least one ace (c) two aces, conditional on getting exactly 3 hearts THE ANSWER IS IN PICTUER. I understand a and b. But in c I dont understand how it became like that especially there are between steps which are not described..can you explian that.

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Four cards (without replay) are drawn from a well-mixed deck of cards (with 52 cards).
What is the probability of getting

(a) exactly two aces
(b) at least one ace
(c) two aces, conditional on getting exactly 3 hearts

THE ANSWER IS IN PICTUER.

I understand a and b. But in c I dont understand how it became like that especially there are between steps which are not described..can you explian that.

 

1. (a)
Let A denote the event "to get exactly two aces"
#g
P(A) =
#m
= 0.025
%3D
(b) Let B denote the event of getting "at least one ace" so that Bc: "none of the cards are aces"
P(B) = 1 - P(B")
#9
1
- 0.2813
#m
(c) Let H denote the event "getting exactly three hearts"
P(A N H)
P(H)
3
P(A|H)
- 0.0178
169
Transcribed Image Text:1. (a) Let A denote the event "to get exactly two aces" #g P(A) = #m = 0.025 %3D (b) Let B denote the event of getting "at least one ace" so that Bc: "none of the cards are aces" P(B) = 1 - P(B") #9 1 - 0.2813 #m (c) Let H denote the event "getting exactly three hearts" P(A N H) P(H) 3 P(A|H) - 0.0178 169
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