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One way to interpret conditional probability is that the sample space of the conditional probability becomes the "conditioning" event. If Event A is drawing a 10 from a deck of cards and Event B is drawing a "spade" from a deck of cards, what would be the sample space for the conditional probability P(A|B)?

User Danja
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1 Answer

23 votes
23 votes

Answer:

The sample space is the set of elements in B i.e n(B) = 13

Step-by-step explanation:

The total number of cards in a deck of cards is 52

The number of cards that carry the number 10 is 4

The number of space cards is 13

The probability of the first event is thus 4/52 = 1/13

The probability of the second event is 13/52 = 1/4

Now, there is only a space card that carries the number 10

This means that the intersection of both events contains a single element in its sample space: n(A n B) = 1

We have the conditional probability as:


P(A|B)\text{ = }\frac{P(A\text{ }\cap\text{ B\rparen}}{P(B)}

Substituting the values, we have it that:


P(A|B)\text{ = }((1)/(52))/((1)/(4))\text{ = }(1)/(52)*4\text{ = }(1)/(13)

The denominator value 13 is the sample space for the conditional probability and that is the n(B) sample space3

User Avelino
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