How would you solve this problem?

Question

There are 85 entrants in a certain contest. Of those 85, only 1 will be eligible for the grand prize. To win the grand prize, the selected individual will draw a single ball from a bag containing 4 balls (only 1 of those balls is red). If the individual selects the red ball, then they win the grand prize. If you are one of the entrants in this contest, what is the probability that you will win the grand prize given that you are the one selected to draw for the grand prize? (hint: assume independent events)

a) 1/384

b) 1/340

c) 1/89

d) 1/85

e) None of the above.

Answer 1

1/85 * 1/4 = 1/340. You have 1/85 chance to be eligible for the grand prize, then you have a 1/4 chance to win it.

However, "given that you are the one selected" assumes that the 1/85 odds have already been beaten, so the only the second step (1/4) matters to the calculation. The answer is (e).

Answer 2

The answer is e) none of the above.

You stipulated that you are the one selected to draw one ball out of a bag containing four balls only one of which is red (the winning ball). So, your chances of getting the red ball are one-in-four. It does not matter that there were 84 other entrants once you are the one selected. There could have been a million others and it still would not have mattered since you were the one select to draw.

Answer 3

Lord, give me strength!

The answer is e) none of the above. Go figure:

4 balls, only 1 is red.

Which is to say 1/4 of the balls are red.

You reach in, you pick: your chances are, oddly enough 1 in 4!

Which is NOT one of the choices. The number of peple from whom YOU were picked, whether 85 or a million, doesn't change the number of red and white balls. The chances are figured on the choices, not the population of choosers.

Any questions?

QED

Answer 4

e)