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25 Sep 2022, 04:07
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D
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Difficulty:
85%
(hard)
Question Stats:
61% (03:35) correct
39%
(03:10)
wrong
based on 139
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A number X is randomly selected from the set of all non-prime integers from 1 to 20 and a number a number Y is randomly selected from the set of all prime numbers from 1 to 20. What is the sum of the probability that product of X and Y is divisible by 7 and the probability that the product of X and Y is divisible by 2?
A. 19/96
B. 25/96
C. 7/12
D. 47/48
E. 1
A. 19/96
B. 25/96
C. 7/12
D. 47/48
E. 1
25 Sep 2022, 10:50
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Aabhash777
There are 8 primes and 12 non primes in first 20 positive integers.
Case I: Probability of product XY to be a multiple of 7.
When X is 14, Y could be any of the 8…….8 ways
When Y is 7, X could be any of the 12…….12 ways
One is common in the above cases when X is 14 and Y is 7, so subtract 1.
Total ways = 12*8 = 96
P= \(\frac{8+12-1}{96}=\frac{19}{96}\)
Case II: Probability of product XY to be a multiple of 2.
When X is any of evens less 2, Y could be any of the 8…….9*8 ways
When Y is 2, X could be any of the 12…….12 ways
9 are common in the above cases when X is any even till 20 and Y is 2, so subtract 9.
Total ways = 12*8 = 96
P= \(\frac{72+12-9}{96}=\frac{75}{96}\)
SUM of Ps = \(\frac{19}{96}+\frac{75}{96}=\frac{94}{96}=\frac{47}{48}\)
D
