# If A is an event,drawing a spade from pack of cards and B an event ' drawing a queen'. f ind the probability of drawing a spade or a queen or both.probability

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### 1 Answer

The probability of drawing a spade is `P(A)=1/4` .(There are 13 spades in a deck of 52 cards. The probability is the number of successes over the number of possibilitites or `13/52=1/4` )

The probability of drawing a queen is `P(B)=1/13` .(There are 4 queens in the deck)

The probability that we draw a spade or a queen is `P(A uu B)`

From the inclusion-exclusion principle we have:

`P(A uu B)=P(A)+P(B)-P(A nn B)`

Now `P(A nn B)=1/4*1/13=1/52`

So `P(A)+P(B)-P(A nn B)=1/4+1/13-1/52=4/13`

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**The probability of drawing a spade or a queen or both is `4/13` **

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This can also be seen by listing all of the possible winners; the 13 spades and the remaining 3 queens. Thus there are 16 "winners" from a total of 52 possibilities, or `16/52=4/13`

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