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Massachusetts Institute of Technology
6.042J/18.062J, Spring ’10: Mathematics for Computer Science Prof. Albert R. Meyer
revised April 26, 2010, 1303 minutes
Solutions to In-Class Problems Week 12, Fri.
Problem 1.
There are two decks of cards. One is complete, but the other is missing the ace of spades. Suppose you pick one of the two decks with equal probability and then select a card from that deck uniformly at random. What is the probability that you picked the complete deck, given that you selected the eight of hearts? Use the four-step method and a tree diagram.
Solution. Let C be the event that you pick the complete deck, and let H be the event that you select the eight of hearts. In these terms, our aim is to compute:
Pr {C ∩ H}Pr {H}
Pr {C | H} =
A tree diagram is worked out below:
cardselected
deckpicked
eet
complete?
8 hearts
1/52
1/2
other
XX
8 of hearts?probability
X
1/104
co
m
pl
51/104
1/2eet
8 hearts
1/51X1/102
Now we can compute the desired conditional probability as follows:
.
cinom
pl
50/102
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