In a bag there are 12 marbles; five blue, four yellow, and three red. Find the f
ID: 3132502 • Letter: I
Question
In a bag there are 12 marbles; five blue, four yellow, and three red. Find the following:
a. The probability of selecting two marbles without replacement and those marbles both being yellow. Another words getting two yellow marbles when selecting two marbles.
b. The probability of selecting two marbles without replacement and not getting two yellow marbles. Another words getting two marbles that are not both yellow.
c. The odds against selecting two yellow marbles when choosing two marbles without replacement.
Explanation / Answer
a)
There are 12 marbles, and 4 are yellow.
Note that the probability of x successes out of n trials is
P(x) = C(N-K, n-x) C(K, x) / C(N, n)
where
N = population size = 12
K = number of successes in the population = 4
n = sample size = 2
x = number of successes in the sample = 2
Thus,
P( 2 ) = 0.090909091 [ANSWER]
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b)
Hence,
P(not 2 yellow) = 1 - P(2 yellow)
= 1 - 0.090909091
= 0.909090909 [ANSWER]
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c)
Hence,
odds against = P(not 2 yellow)/P(2 yellow)
= 0.909090909/0.090909091
= 10:1 [ANSWER]