jmc

Question

On the number line, point A is located at 0, point B is located at 4, and point C is located at 6. FIGURE A dart randomly lands somewhere on the number line between A and C. What is the probability that it lands closer to B than it does to A or C?

Accepted Answer

First, suppose that the dart lands between

A

and

B

. It then has a probability of 1/2 of being closer to

A

than to

B

, and it is always closer to

B

than it is to

C

, so it is closer to

B

than it is to

A

and

C

with probability 1/2.

On the other hand, if it lands between

B

and

C

, then it is definitely closer to

B

than to

A

, and it has a probability of 1/2 of being closer to

B

than to

C

. As before, it is closer to

B

than it is to

A

and

C

with probability

1/2

.

In either case, the probability that the dart lands closest to

B

is 1/2, so the probability overall is

\frac{1}{2}

.