5.) Solve the following: A. 9 yellow balls and 5 red balls are placed in an urn.
ID: 3340841 • Letter: 5
Question
5.) Solve the following:
A.
9 yellow balls and 5 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?
a) 0.5600
b) 0.6429
c) 0.4286
d) 0.3846
e) 0.7222
f) None of the above.
B.
There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 6 chocolate chip and 12 sugar cookies. The green jar contains 5 chocolate chip, 7 sugar and 9 peanut butter cookies. The pink jar contains 15 chocolate chip, 11 sugar and 8 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are 12 , 14 , and 14 , respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?
a) 0.2444
b) 0.1078
c) 0.3235
d) 0.0809
e) 0.1626
f) None of the above.
C.
An experiment consists of choosing an urn with the following probabilities that Urn 1, Urn 2, or Urn 3 will be chosen: 1/2, 1/4, and 1/4, respectively. Urn 1 contains 7 brown marbles and 12 clear marbles. Urn 2 contains 9 brown marbles, 15 clear marbles and 6 red marbles. Urn 3 contains 10 brown marbles, 14 clear marbles and 5 red marbles.
A marble is then chosen from the chosen urn. What is the probability that Urn 3 was chosen, given that the marble chosen was clear?
a) 0.4828
b) 0.2149
c) 0.1207
d) 0.1609
e) 0.2990
f) None of the above.
Explanation / Answer
A) Probability of the second ball being yellow is computed as:
= Probabiltiy that first ball is red and second ball is yellow + Probability that both balls drawn are yellow
= (5/14)*(9/13) + (9/14)*(8/13)
= 0.6429
Now given that the first ball is yellow, probability that the first ball is red is computed as:
= Probabiltiy that first ball is red and second ball is yellow / Probability of the second ball being yellow
= (5/14)*(9/13) / 0.6429
= 0.3846
Therefore d) 0.3846 is the required probability here.
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