SOLUTION: A deck of cards has 6 gray, 5 navy, and 6 yellow cards. You pick 4 cards from the deck. Cards are not returned to the deck after they are picked. P(the first card is not gray, t
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Question 29565: A deck of cards has 6 gray, 5 navy, and 6 yellow cards. You pick 4 cards from the deck. Cards are not returned to the deck after they are picked. P(the first card is not gray, the second card is gray, the third card is yellow, and the fourth card is gray).
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
start: 6G/5N/6Y
This is quite a nasty question. All four questions are dependent... what comes before affects what comes after.
The best way to draw this is a probability tree, but it gets very "busy" by the third "branch". Added to that...I cannot draw one here for you, as the graphics are not upto doing that.
P(first is not grey) = P(first is navy) + P(first is yellow)
P(first is not grey) = P(N) + P(Y)
P(first is not grey) = 5/17 + 6/17
P(first is not grey) = 11/17
P(first is not grey) = 0.6471
Note the way i have built up the subsequant answers with "and" being multiply. I have also kept track of how many cards of each colour i have, for each of the 2 possible branches of the tree...which stem from the first part of the question.
The tree is useful as a visual aid to keeping the correct probabilities going along each branch.
2. P(second is grey) = P(first was navy and second is grey) + P(first was yellow and second is grey)
P(second is grey) = P(NG) + P(YG)
P(second is grey) = (5/17 * 6/16) + (6/17 * 6/16)
P(second is grey) = 15/136 + 9/68
P(second is grey) = 33/136
P(second is grey) = 0.2426
3. P(third is yellow) = P(first was navy and second was grey and third is yellow) + P(first was yellow and second was grey and third is yellow)
P(third is yellow) = P(NGY) + P(YGY)
P(third is yellow) = (5/17 * 6/16 * 6/15) + (6/17 * 6/16 * 5/15)
P(third is yellow) = 3/68 + 3/68
P(third is yellow) = 6/68
P(third is yellow) = 3/34
P(third is yellow) = 0.0882
4. P(fourth is grey) = P(first was navy and second was grey and third was yellow and fourth is grey) + P(first was yellow and second was grey and third was yellow and fourth is grey)
P(fourth is grey) = P(NGYG) + P(YGYG)
P(fourth is grey) = (5/17 * 6/16 * 6/15 * 5/14) + (6/17 * 6/16 * 5/15 * 5/14)
P(fourth is grey) = 15/952 + 15/952
P(fourth is grey) = 30/952
P(fourth is grey) = 15/476
P(fourth is grey) = 0.0315
jon.
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