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A cube with its sides numbered 1 through 6 is rolled twice, first land
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10 Jul 2021, 03:50
Solution:
The total number of possibilities will be 6 x 6=36.
And out of this 36 number only 2(1+1) and 12(6+6) can be computed in 1 ways rest all others can be computed in different ways.
Thus, the range of the numbers also lie between 2-12.
Prime numbers between 2-12= 2, 3, 5, 7, 11
2 can be formed in 1 way= 1+1=2
3 can be formed in 2 ways= 1+2 & 2+1
5 can be formed in 4 ways= 1+4, 4+1, 2+3, 3+2
7 can be formed in 6 ways= 1+6, 6+1, 2+5, 5+2, 3+4, & 4+3
11 can be formed in 2 ways= 6+5 & 5+6
Therefore the above sums up to 15 possible ways
Probability that a + b is prime= \(\frac{Total number of ways the sum is prime}{ Total number of all possibilities}\)=
=\(\frac{15}{36}\)=\(\frac{5}{12}\)
IMO C
Hope this helps!