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Answer:
6. 15/22
7. 1/12
9. 1/16
10. 0
Step-by-step explanation:
6. 10 of the 12 tiles are "not P", so the probability of a "not P" on the first draw is 10/12 = 5/6. After drawing a "not P" on the first draw, 9 of the remaining tiles are "not P". The probability of drawing one of those is 9/11. So, the joint probability of drawing two "not P" tiles is ...
(5/6)(9/11) = (5·9)/(6·11) = 15/22
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7. The probability of drawing a tile worth 3 points is 3/12 = 1/4. The probability of drawing a tile worth 1 point is 4/12 = 1/3. So, the joint probability of drawing a 3-point tile, then a 1-point tile is ...
(1/4)(1/3) = 1/12
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9. There are 3 of the 12 tiles worth more than 4 points. The probability of drawing one of them is 3/12 = 1/4. The probability of doing it again is also 1/4, so the probability of doing it twice is ...
(1/4)(1/4) = 1/16
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10. The probability of drawing a Z is 1/12. Having drawn a Z, the probability of drawing a 10-point tile is 0/11. The joint probability of drawing a Z twice is ...
(1/12)(0/11) = 0
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Additional comment
We revisited problem 7 because we needed that answer for problem 9.
