Answer:
1/7
Explanation:
If I choose a number from the integers 1 to 25, the total number of integers I can pick is the total outcome which is 25. n(U) = 25
Let the probability that the number chosen at random is a multiple of 6 be P(A) and the probability that the number chosen at random is is larger than 18 be P(B)
P(A) = P(multiple of 6)
P(B) = P(number larger than 18)
A = {6, 12, 18, 24}
B = {19, 20, 21, 22, 23, 24, 25}
The conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is expressed as P(A|B).
P(A|B) = P(A∩B)/P(B)
Since probability = expected outcome/total outcome
A∩B = {24}
n(A∩B) = 1
P(A∩B) = n(A∩B)/n(U)
P(A∩B) = 1/25
Given B = {19, 20, 21, 22, 23, 24, 25}.
n(B) = 7
p(B) = n(B)/n(U)
p(B) = 7/25
Since P(A|B) = P(A∩B)/P(B)
P(A|B) = (1/25)/(7/24)
P(A|B) = 1/25*25/7
P(A|B) = 1/7
Hence the conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is 1/7