C 2.4-17 (Mar 1) et S be the set of sequences of seven cards, in which no Questi

Question

C 2.4-17 (Mar 1) et S be the set of sequences of seven cards, in which no Question 5 4 pts Exercise Matching.E This problem describes an experiment in which conditional probabilities are used to compute "proper" probability. The experiment starts with two urns. Urn #1 contains 2 white marbles and 5 black marbles. Urn #2 contains 3 white marbles and 7 black marbles. One marble from each urn is drawn at random. (For each urn, the chance of each marble being drawn is the same.) Let T be the event that the two marbles are the same color. Let w be the event that the marble from Urn #1 is white. Find P (T). Question 6 4 pts Let S be the set of sequences of seven cards, in which no card is repeated. You can think of it as all the ways to deal seven cards, where the order of the deal matters. What is the size of S ? (You may give your answer as a product.)

Explanation / Answer

Question 5:

Number of marbles in first urn is

2 +5 = 7

Number of marbles in second urn is

3+7=10

The probability that a white marble is selected from URN 1 is

P(white from urn 1) = 2/7

The probability that a white marble is selected from URN 2 is

P(white from urn 2) = 3/10

So the probability that both white marbles are selected is

P(both white) = P(white from urn 1)P(white from urn 2)=(2/7) * (3//10) = 3/35

Likewise the probability that both black marbles are selected is

P(both black) = P(blackfrom urn 1)P(blackfrom urn 2)=(5/7) * (7//10) = 1/2

So the probability that tw marbles are of the same colors is

P(T) = P(both white) + P(both black) = (3/35) + (1/2) = 41/70=0.5857

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