Question

One card is selected from a deck of cards. Find the probability of selecting a black card or a card less than 8.

I did it this way:

P(B or <8) = P(B) + P(<8) - P(B and <8)
= (13/52) + (28/52) - (7/52)
= 34/52
= 17/26

The homework key says it's 10/13?

What am I doing wrong?

Answer 1

Is an ACE the highest card or the lowest card?

Answer 2

lowest

Answer 3

Thanks I will start working on this with you but I'm not the best with probabilities.

Answer 4

P(black) = 1/2
P( <8) = 28/52 = 7/13

Answer 5

Probability isnt my forte either

Answer 6

OK, duh! I was thinking of spades. So, that gives me

P(B or <8) = P(B) + P(<8) - P(B and <8)
= (26/52) + (28/52) - (7/52)
= 47/52

Which is still different than the key.

Answer 7

I got 7/13 also. but I'm not sure. I am fairly confident it isn't 10/13.

Answer 8

Oh crap, I was counting spades again. He's the solution.

P(B or <8) = P(B) + P(<8) - P(B and <8)
= (26/52) + (28/52) - (14/52)
= 40/52
= 10/13

Answer 9

how did you get 14/52?

Answer 10

There are 7 spades less than 8 (A, 1,2,3,4,5, 6,7) and 7 clubs. That's 14 cards less than 8.

Answer 11

AH I see!

Answer 12

weshfella, your 1/2 above helped me figure out I was miscounting. Thanks!

Answer 13

yw

Answer 14

for some reason I was thinking = 8 rather than < 8 !!!!