About 15% of United Kingdom residents bet on at least one horse race annually. C
ID: 3042415 • Letter: A
Question
About 15% of United Kingdom residents bet on at least one horse race annually. Census data indicate that 48.4% of the adult population in the UK is male.
Assuming that betting is independent of gender, compute the probability that a UK adult selected at random is a male and bets on horse racing.
Using the result in part (a), compute the probability that a UK adult selected at random is male or bets on horse racing.
A recent poll indicated that 10.4% of adults in the UK are males and bet on horse racing. What does this indicate about the assumption in part (a)?
How will the information in part c) affect the probability you computed in part (b)?
Explanation / Answer
Solution:-
a) The probability that a UK adult selected at random is a male and bets on horse racing is 0.0726.
P(A) = 0.15
P(B) = 0.484
P(A and B) = P(A) × P(B)
P(A and B) = 0.15 × 0.484
P(A and B) = 0.0726
b) The probability that a UK adult selected at random is male or bets on horse racing is 0.5614.
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.15 + 0.484 - 0.0726
P(A or B) = 0.5614.
c)
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.15 + 0.484 - 0.104
P(A or B) = 0.53