1. Solve the following regarding probability. A. Suppose that 7 green balls and
ID: 3361493 • Letter: 1
Question
1. Solve the following regarding probability.
A.
Suppose that 7 green balls and 13 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that both balls drawn have the same color if the first ball is replaced before the second is drawn?
a) 0.2275
b) 0.1225
c) 0.0650
d) 0.5450
e) 0.4225
f) None of the above.
B.
Urn A contains 9 yellow balls and 6 red balls. Urn B contains 5 yellow balls and 12 red balls. Urn C contains 11 yellow balls and 12 red balls. An urn is picked randomly (assume that each urn is equally likely to be chosen), and then a ball is picked from the selected urn. What is the probability that the chosen ball came from urn B, given that it was a yellow ball?
a) 0.0528
b) 0.3485
c) 0.0549
d) 0.4372
e) 0.2143
f) None of the above.
C.
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.
Explanation / Answer
Question 1:
Probability that both the balls drawn are of the same colour is computed as:
= Probability of drawing both the green balls + Probability of drawing both the purple balls
The probability remains the same for drawing a ball because we are drawing the balls with replacement.
= (7/20)2 + (13/20)2
= 0.545
Therefore d) 0.545 is the required answer here.
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