O.02sp) A container has 5 blue marbles, 3 red marbles, and 6 white marbles. If 3
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Question
O.02sp) A container has 5 blue marbles, 3 red marbles, and 6 white marbles. If 3 marbles are drawn with replacement, what is the probability that all three will be blue? 3. rea olwhrle A poll states that 35% of the workers in a large company have new computers. If 4 workers are selected at random, what is the probability that at least one worker has a new computer? 4, In a shipment of 30 televisions, 3 are defective. If 2 TV sets are randomly selected and tested without replacement, what is the probability that both are defective? 5.Explanation / Answer
3)
Total marbles in the container = 5 + 3 + 6 = 14
P( Blue marble) = n( Blue marbles) / n( Total marbles) = 5 / 14
P( All three marbles are blue) = 5/14 * 5/14 * 5/14
= 0.0456
4)
X ~ Binomial(n,p) = Binomial(4 , 0.35)
Where n = 4 and p = 0.35
Binomial probability distribution is
P(X) = nCx px (1-p)n-x
P( X >= 1) = 1 - P( X = 0)
= 1 - 4C0 0.350 0.654
= 1 - 0.1785
= 0.8215
3)
P( Defective item) = 3 / 30
P( First defective item) = 3/30
Since second item drawn without replacement, there are 29 total TV sets are remaining with 2 defective.
P( Second defective item) = 2 / 29
P( Both defective items) = 3 / 30 * 2 / 29
= 0.0069
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