Answer:
9) 1/42
10) 1/14
Explanation:
The probability of the compound event is the product of the probabilities of the parts. Note that the first draw (without replacement) modifies the probability of associated with the second draw.
9.
5 is one of 7 tiles. After drawing 5, 6 is one of 6 tiles.
P(5 then 6) = P(5) × P(6 | 5) = 1/7 × 1/6 = 1/42
10.
There are 3 odd tiles among the 7. After drawing one of them, 20 is one of 6 tiles.
P(odd then 20) = P(odd) × P(20 | odd) = 3/7 × 1/6 = 3/42 = 1/14
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Alternatively, you can consider the number of permutations of 2 tiles out of 7. That is P(7, 2) = 7!/(7-2)! = 7·6 = 42. Then the trick is to count how many of them will be the sequence of interest.
5 then 6: Among the 42 ways 2 tiles can be drawn, there is only one that is the required sequence: P(5,6) = 1/42.
odd then 20: There are 3 odd numbers, so the possible sequences of interest are (5,20), (7,20), (9,20). That is, there are 3 of 42 sequential draws that match the criteria. P(odd,20) = 3/42 = 1/14.