SOLUTION: I'm stuck on a problem. I've tried working it and come close to the answer, but not sure where I am going wrong. The question is: A board game uses a deck of 20 cards and two cards

Question 1149544: I'm stuck on a problem. I've tried working it and come close to the answer, but not sure where I am going wrong. The question is: A board game uses a deck of 20 cards and two cards are drawn at random. Determine the probability that neither card shows a 3 or 5, both with and without replacement. The table consists of 5 rows and each row is numbered 1,2,3,4,5 horizontally. The formula I used was: P (A and B) = P(A) * P(B) = and got a fractional answer of 1 over 25 with replacement and I used the same formula for without replacement and got a fractional answer of 3 over 95. However, Im being told both my answers are wrong & that the correct answers are 9 over 25 with replacement and 33 over 95 without replacement. Can someone help me understand what Im doing wrong? Thank you so much! :)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Your presentation of the problem SUGGESTS that the deck of 20 cards consists of 4 cards each with the numbers 1, 2, 3, 4, and 5; but you don't make that clear. However, a deck like that would produce what you are being told are the correct answers to the problem.

Then the correct use of your formula P(A)*P(B) will give you those answers.

You want the probabilities that each card drawn is NOT either a 3 or a 5.

With replacement, P(A) and P(B) are both 12/20 = 3/5.

Without replacement, P(A) is 12/20 = 3/5 and P(B) is 11/19.

Use those probabilities to get the given correct answers.

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