Problems on
Probability:
1. Two dices are
tossed. The probability that the total score is not a prime number is:
Solution:
n(S) = 36.
n(E)
={(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}
P(getting a prime number) = n(E)/ n(S)
= 15/36
= 5/12.
P(not getting a prime number) = 1-5/12
= 7/12.
2. A speaks truth in
60% cases and B in 70% of the cases. In what percentage of cases are they
likely to contradict each other, narrating the same incident?
Solution:
P(A)
=60/100 =3/5.
P(A̅) = 1-3/5 = 2/5.
P(B)=70/100 =7/10.
P(B̅)= 1-7/10 =3/10
Since they contradict each other while
narrating the same incident. We get,
P(A)*P(B̅) + P(A̅)+P(B) = 3/5 * 3/10 + 2/5 * 7/10
= 9/50 + 14/50
= 23/50.
The
percentage will be (23/50) *(100) = 46%.
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