Question

Yoshi picks a point on the number line between 2 to 8. What is the probability that it is closer to the point 4 than to either end?

Answer 1

The answer is 1/2. There are 3 ways for this to happen and 6 possibilities. 3/6 = 1/2

Answer 2

The probability that it is closer to the point 4 than to either end is:

`(1)/(2)`

Explanation:

If we divide the number line between 2 to 8 into 6 equal parts i.e. 2-3-4-5-6-7-8

Then the number is closer to the point 4 than to the either end if it will lie in the part:

3-4-5-6

( Because if it will lie between 2-3 then it will be close to 2 and not to 4.

If it will lie between 6-7 or 7-8 then it will be close to 8 and not close to 4)

Hence, the number of parts the number may lie such that it is close to 4 is: 3

and the total number of parts are: 6

Hence, the probability that the number is close to 4 than to either end is the ratio of the number of parts where it is close to 4 to the total number of parts.

i.e.

The probability is:

`Probability=(3)/(6)\\\\i.e.\\\\Probability=(1)/(2)`