q: An archer is shooting arrows from various distances. She shoots at a target from 60 yards, 70 yards, and 80 yards. The probability that she hits within the bullseye from 60 yards is 2/3, the probability that she hits within the bullseye from 70 yards is 3/5, and the probability that she hits within the bullseye from 80 yards is 1/2. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 19/20
(B) 29/30
(C) 49/50
(D) 9/10
(E) 14/15
a: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 60 yards)*(prob that she misses from 70 yards)*(prob that she misses from 80 yards)
Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5; Prob that she misses from 80 yards = 1 - 1/2 = 1/2
Thus the probability that she misses all shots = (1/3)*(2/5)*(1/2) = 2/30 = 1/15
Thus the probability that she makes at least one shot = 1 - (1/15) = 14/15 The answer is (E).
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q: How many ways someone can make with 8 shirts and 6 pants?
Options:
(A) 50
(B) 45
(C) 55
(D) 52
(E) 48
a: If you can only wear one shirt and one pair of pants, then you can make 8*6 = 48 combinations. The answer is (E).
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q: An analyst will recommend a combination of 1 industrial stocks, 1 transportation stocks, and 1 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 3 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
a: 5C1 * 4C1 * 3C1 = 5*4*3 = 60. The answer is (C).
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q: If 10 crates have 96 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 5
(B) 10
(C) 40
(D) 20
(E) 0
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Each crate requires 4 apples and totally there are 10 crates so required apples = 10 * 4 = 40 The answer is (C).
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