0 -1 points TanFin12 7.6.018 CML Urn A contains three white balls and seven blac

Question

0 -1 points TanFin12 7.6.018 CML Urn A contains three white balls and seven black balls. Urn B contains four white balls and five black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probebility that the transferred ball was white given that the second ball drawn was white? (Round your answer to three decimal places.) Need Help? Iliin -12 points TanFin12 7.6.021 CML -belt law re shown in the accompanying Data compiled by the Highway Patrol Department regardng the use of seat-belts by drivers in a certain area after the passage of a compulsory table. (Round your answers to three decimal places.) Percentage of Drivers in Group Percent of Group Stopped for Moving Vielation Drivers Group I (using seat-belts) Group II (not using seat-belts) 0,3 45 (a) If a driver in that area is stopped for a moving violation, what is the probability that he or she will have a seat-belt on? (b) If a driver in that area is stopped for a moving violation, what is the probablity that he or she will not have a seat-belt on?

Explanation / Answer

Total number of ball in urn A is : 3+7 = 10

Let W1 be the event that a white ball is drawn from urn A and B1 shows the event that a black ball is drawn from urn B. So,

    P(W1) = 3/10, P(B1) = 7/10

Let W2 shows the event that a white ball is drawn from urn B and B2 shows the event that a black ball is drawn from urn B.

The total number of balls in urn B is 4+5 = 9

The conditional probabilites:

P(W2|W1) = 10/9, P(W2 | B1) = 5/9

By the law of total probability, the probability that a white is drawn from second urn is

P(W2) = P(W2|W1) P(W1) + P(W2 | B1) P(B1)

           = (10/9)*(3/10) + (5/9)*(7/10)

           = 1/3 + 7/18 = 0.722

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