Question 1191534: There are n amount of balls in a basket, numbered from 1,2,… 14. Randomly two balls are taken out one after another with replacement. a) What is the probability of the sum of two balls being greater than 22? b) It is made sure that first ball taken out is even - what is the probability of the sum being more than 10 now?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! there are 196 possibilities, 14 for the first ball and 14 for the second.
for 11 as the first choice, there are 3 possibilities for the second, 12,13,14
for 12 as the first choice, there are 4 for the second 11-14
for 13, there are 5 for the second, 10-14
for 14, there are 6 for the second.
That is 18 possibilities.
The order can be reversed, and that is 18 more, for 36
The probability is 36/196 or 9/49.
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2,4,6,8,10,12,14
3/7 possibility the first ball is 10 or more, in which case the second ball will make the sum >10.
4/7 possibility that the first ball is 2,4,6,8
if 2,the second ball has to be >=9 so the probability is (1/7)(6/14)=3/49
if 4,the second ball has to be >=7 probability jointly is (4/49)
if 6, then has to be >=5 and joint is 5/49
if 8, then has to be >=3 and joint is 6/49.
The total is 39/49 probability.
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