Question

A student solves a problem correctly 40 times out of 72 tries. Based on this data, what is the probability that the student incorrectly solves the next problem? Enter your answer in the box as a percent rounded to the nearest whole number.

Answer 1

The probability of the student incorrectly solves the next problem is 44%.

Explanation:

Let E be the event of solving a problem correctly.

Then E' is the event that the problem is solved incorrectly.

Now, recall the definition of probability.

probability of an event =
`(number of favorable events)/(total number of events)`

So,

p(E) =
`(40)/(72)`

Also,

p(E) + p(E') = 1 and

p(E') = 1 - p(E)

= 1 -
`(40)/(72)`

=
`(72-40)/(72)`

=
`(32)/(72)`

=
`(4)/(9)`

=
`(4)/(9) (100)`

= 44% rounded.

Hence, the probability of the student incorrectly solves the next problem is 44%.