# Conditional Probability Question?

1. A die is rolled. What is the probability that it is a 5, given it is greater than 3?

- Would I do P(5)= n(1)/n(60

= 1/6?

2. A card is drawn from a deck of cards. What is the probability that it is a jack if you know that it is a face card?

- Thanks!

Relevance

P1 = 1/3

P2 = 1/4 (if Ace is a face card, else 1/3)

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• Let x be the roll.

It can't be 1/6, since we already known the die is going to be 4,5 or 6 (we're given X>3). Since it can only be 1 of these 3 values, our answer is 1/3.

Formally, we could also use:

P(X=5|X>3)=

P(X=5 and X>3)/P(X>3)=

P(X=5)/P(X>3)=(1/6)/(3/6)=1/3

Note the intersection of event "X=5 and X>3", which reduces to "X=5" because this satisfies both event X=5 as well as X>3.

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Similarly,

P(jack|face card)=

P(jack and face card)/P(face card)=

P(jack)/P(face card)=

(4/52)/(12/52)=1/3

Of course in general, conditional probabilities don't reduce like that. But in these cases they do, because the numerator event is a subset of the denominator event.

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