Archie builds a pool in his backyard. The pool measures 16 yards long, 6 yards wide and 2 yards deep. How many gallons of water
1 answer:
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Answer:
- <em>Probability of event A: </em>1<u>/504</u>
- <em>Probablity of event B:</em> <u>1/84</u>
Explanation:
1. Event A: Bob is the first prize winner, Lena is second, and Ann is third,
- The probability that Bob is the first prize winner is one outcome out of 9 possible outcomes, so it is 1/9
- The probability that Lena is second, after Bob is the first prize winner is one outocome out of 8 possible outocmes, so it is 1/8
- The probability Ann is third, after Bob y first and Lena is second is 1/7.
Thus, the joint probability that Bob is the first prize winner, Lena is second, and Ann is third is the product of the three calculated probabilities:
- 1/9 × 1/8 × 1/7 = 1 / (9×8×7) = 1/504 ← answer
2. Event B: The first three prize winners are Soo, Omar, and Kira, regardless of order
When the order does not matter, the number of combinations for three different persons win the 3 prizes is C(3,3), which is computed with the corresponding formula:
Thus:
And the number of possible combinations of winners is C(9,3):
Then, the probability is the number of favorable combinations, C(3,3) = 1, divided by the number of possible combinations, C(9,3) = 84:
- 1/84 ← answer