Question

​70% of the workers at Motor Works are​ female, while 68​% of the workers at City Bank are female. If one of these companies is selected at random​ (assume a​ 50-50 chance for​ each), and then a worker is selected at​ random, what is the probability that the worker will be​ female?

Answer 1

69%

Explanation:

If Motor Works is selected, the probability that the worker is a female is 70%. If City Bank is selected, the probability is 68%.

But we don't know what company will be selected, we only know that they have the same probability, 50-50.

So, with 50% of probability the worker will be female with a 70% of probability (because they selected from Motor Works) and with 50% of probability the worker will be female with a 68% of probability (they selected from City Bank).

We express this as 50%*70% + 50%*68% = 69%

The multiplication means that both probabilities happen together and the sum means that happens one thing or the other (they select Motor Works or City Bank)