An urn contains 6 red balls and 3 blue balls. One ball is selected at random and is replaced by a ball of the other color. A second ball is than chosen. What is conditional probability that the first ball selected is red, given that the second ball was red?
Answers
Answer:
2/9 is the answer
thank you
10/17 is conditional probability that the first ball selected is red, given that the second ball was red
Step-by-step explanation:
An urn contains 6 red balls and 3 blue balls
Let say first ball Selected is Red
the Probability = 6/9 = 2/3
Then Balls in Urn = 5 Red Balls + 4 Blue Balls
Probability of Red Balls = 5/9
Probability of Red Ball in case 1 = (2/3)(5/9) = 10/27
Let say first ball Selected is Blue
the Probability = 3/9 = 1/3
Then Balls in Urn = 7 Red Balls + 2 Blue Balls
Probability of Red Balls = 7/9
Probability of Red Ball in case 1 = (1/3)(7/9) = 7/27
Probability of Red Ball = 10/27 + 7/27 = 17/27
Probability of red ball when first ball selected was red = 10/27
conditional probability that the first ball selected is red, given that the second ball was red = (10/27)/(17/27)
= 10/17
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