Question

If 2 cards are drawn from a deck of 52 cards, what is the expected number of spades?
A. 0.75

B. 0.25

C. 0.50

D. 0.47

Answer 1

im confuse on how to solve this?

Answer 2

2/52 = 0.25 I think :PP

Answer 3

i tried that its wwrong

Answer 4

You need a weighted average over all possible card pair choices. Try the following scheme:\[\text{Average number of spades}=\frac{\displaystyle \sum_{\text{all posible pairs}} \text{Number of spades in each pair}}{\text{Total number of card pairs}}\]Does that make sense?

Answer 5

@yakeyglee does it work if I draw a table? Something similar when you are asked a "throwing a dice" question.

Answer 6

@mirella sorry about that :P

Answer 7

I mean, in theory, yes, but good luck making a \(52 \times 52\) grid, minus the main diagonal. Haha. You're better off trying to crafty up algebraic expressions for the numerator and denominator above.

Answer 8

*craft up

Answer 9

haha, good point! but why can't I use 13/52 x 12/51 to find the number of spades, assuming the cards are being replaced.

Answer 10

I think you mean "assuming the cards aren't being replaced". The reason is because that gives you the probability of drawing two spades, not the average number of spades. The number you're trying to find isn't even a probability (though you DO need to use concepts from probability, most notably, combinations).

Answer 11

"Average number of spades over all allowed choices." is really equivalent to the "expected number of spades". The expression I gave is really just an average over all possible choices.

Answer 12

Oh I think I get it, thank you! I normally suck in probability...