Probability involving 'EITHER OR'

Ian Stewart wrote:

dtweah wrote:In a town of 3000 people, 600 are over 50 years old and 1000 are female. It is known that 30% of the female are over 50 years. What is the probability that the person chosen at random is either a female or over 50 years?

A. 11:13

B. 13:17

C. 2:3

D. 9:17

E. 13:9

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The correct answer isn't there. The answer choices are expressed in terms of what are known as 'odds' (the ratio of good outcomes to bad ones). A probability is the ratio of good outcomes to *all* outcomes, and thus is always between 0 and 1.

Here we have 1000 women, 30% of whom are over fifty years old, so we have 300 women over fifty. We must therefore have 300 men over fifty. Adding these 300 over-fifty men to the 1000 women, there are thus 1300 people who are either female or over fifty, and the probability of selecting such a person is 1300/3000 = 13/30.

I'm sure B is *intended* to be the correct answer here, but it is not written correctly. It's a dodgy question.

Ian Stewart wrote:
The correct answer isn't there. The answer choices are expressed in terms of what are known as 'odds' (the ratio of good outcomes to bad ones). A probability is the ratio of good outcomes to *all* outcomes, and thus is always between 0 and 1.

Here we have 1000 women, 30% of whom are over fifty years old, so we have 300 women over fifty. We must therefore have 300 men over fifty. Adding these 300 over-fifty men to the 1000 women, there are thus 1300 people who are either female or over fifty, and the probability of selecting such a person is 1300/3000 = 13/30.

I'm sure B is *intended* to be the correct answer here, but it is not written correctly. It's a dodgy question.