Question

Tim’s goal is to run one marathon in each of the 50 states. To determine the order in which he will run the marathons, he will write the name of each state on a slip of paper and place the slips of paper in a bowl. He will then draw the names of the states one at a time from the bowl until all the slips of paper have been drawn.

If there are 26 states east of the Mississippi River and 24 states west of the Mississippi River, what is the probability that the third state drawn will be east of the Mississippi, given that the first one drawn was east of the Mississippi and the second one drawn was west of the Mississippi?

A) 1/2
B) 13/24
C) 13/25
D) 25/48

Answer 1

I belive the answer is D or B (it is most likely D due to how the probability seems to be more accurate than B)

We know that it is not C because if we times it by two we get 26/50 which is not correct due to the total amount of states.

Answer A is not it because that is a half change when east has a larger chance.

The answer D may be the correct answer as well as for B since they both are more than half the entrees. But B has a little less than probability as compared to the answer D

Answer 2

This is a conditional probability issue, so the original probability of 26/50 no longer prevails. There have been changes in both the numerator and the denominator.

The third marathon will be chosen from 48 states, 25 east of the Mississippi and 23 west of the Mississippi. The probability will be 25/48.

so your answer is D) 25/48