Question 320889: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
a)create a tree diagram for this experiment, with the twig probabilities
b) what is the probability that one or more of the 3 cards picked is a face card?
c)what is the probability that you get exactly 3 face cards, given that you did get 1 or more face cards?
Answer by toidayma(44)   (Show Source):
You can put this solution on YOUR website! We have 26 black cards, 6 of them are face cards, 20 of them are not face cards. Of course.
a> here is the diagram, hope you can understand.
<---1st picking---> <---2nd picking---> <---3rd picking--->
face card: 6/10 face card: 5/25 face card: 4/24
normal card: 20/24
normal card: 20/25 face card: 5/24
normal card: 19/24
normal card: 20/26 face card: 6/25 face card: 5/24
normal card: 19/24
normal card: 19/25 face card: 6/24
normal card: 18/24
b> The probability of one or more of three cards picked is face card = 1 - the probability of all the picked cards are normal cards.
You can see in the diagram that the probability of all the three picking are normal cards is: (20/26)(19/25)(18/24).
So the finding probability is 1 - (20/26)(19/25)(18/24)
c>Actually, I dont really remember how to solve this kind of question :-( but I think that I would solve this way:
Given that you did get 1 face card -> the probability of getting two more face cards is: (5/25)(4/24)
Given that you did get 2 face cards -> the probability of getting one more face card is (4/24)
So, the probability of getting three face cards given that you get one or more face card is (5/25)(4/24) + (4/24).
I think I get the last solution wrong, so you should post the last problem again to get help from other tutors. I am sorry for this.
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