SOLUTION: A box contains 74 brass washer, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement. a) Determine the probability that

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Question 169882: A box contains 74 brass washer, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement.
a) Determine the probability that all three are steel washers.
b) Determine the probability that there are no aluminium washers drawn, when three washers are drawn at random from the box without replacement.
c) Find the probability that there are two brass washers and either a steel or an aluminium washer when three are drawn at random, without replacement.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A box contains 74 brass washer, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement.
a) Determine the probability that all three are steel washers.
# of ways to succeed = 86C3
# of possible outcomes = 200C3
P(success) = 86C3/200C3 = 0.0779...
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b) Determine the probability that there are no aluminium washers drawn, when three washers are drawn at random from the box without replacement.
# of ways to succed = 114C3/200C2
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c) Find the probability that there are two brass washers and either a steel or an aluminium washer when three are drawn at random, without replacement.
# of ways to succeed:
Draw to brass washers in 74C2 ways
Draw a steel or aluminum washer 126 ways
Total # of ways to succeed 74C2*126
Prob of success: [74C2*126]/[200C3] = 0.25912
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Cheers,
Stan H.

Answer by Edwin McCravy(20059) (Show Source):
You can put this solution on YOUR website!
Warning: Stanbon's
(b) and (c) are incorrect.
Edwin's solution:
A box contains 74 brass washer, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement.
a) Determine the probability that all three are steel washers.

There are 86 steel washers. There are or washers. So the desired probability is 86 choose 3 ------------ 200 choose 3

b) Determine the probability that there are no aluminium washers drawn, when three washers are drawn at random from the box without replacement.

There are 74+86 or 160 non-aluminum washers. (This can also be calculated by subtracting the 40 aluminum washers from the total 200, i.e., 200-40=160.) 160 choose 3 -------------- = 200 choose 3

c) Find the probability that there are two brass washers and either a steel or
an aluminium washer when three are drawn at random, without replacement.

There are 74 brass washers. There are 86+40 or 126 washers that are either steel or aluminum. So the desired probability is (74 choose 2) + (126 choose 1) -------------------------------- = 200 choose 3 Edwin