A number is selected at random from first 100 whole numbers. Find
the probability that the number is divisible by 8 or 12.
Answers
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Answer:
Required probability = 4/25
Step-by-step explanation:
A number can be chosen at random from the first 100 whole numbers in 100 ways and this is the number of outcomes in the event space.
Let A be the event - 'the number selected is divisible by 8' and B be the event - 'the number selected is divisible by 12'.
Then AB is the event - 'the number selected is divisible by both 8 or 12, i.e., divisible by 24'.
Number of outcomes favourable to the event A is
n(A) = [ 100/8 ] = 12
Similarly n(B) = [ 100/12 ] = 8
and n(AB) = [ 100/24 ] = 4
Thus P(A) = 12/100, P(B) = 8/100 & P(AB) = 4/100
Required probability is = P(A + B)
= P(A) + P(B) - P(AB)
= 12/100 + 8/100 - 4/100
= 16/100 = 4/25
Required probability = 4/25
A number can be chosen at random from the first 100 whole numbers in 100 ways and this is the number of outcomes in the event space.
Let A be the event - 'the number selected is divisible by 8' and B be the event - 'the number selected is divisible by 12'.
Then AB is the event - 'the number selected is divisible by both 8 or 12, i.e., divisible by 24'.
Number of outcomes favourable to the event A is
n(A) = [ 100/8 ] = 12
Similarly n(B) = [ 100/12 ] = 8
and n(AB) = [ 100/24 ] = 4
Thus P(A) = 12/100, P(B) = 8/100 & P(AB) = 4/100
Required probability is = P(A + B)
= P(A) + P(B) - P(AB)
= 12/100 + 8/100 - 4/100
- = 16/100 = 4/25