Question

Data released by the dept of education regarding the rate of ninth grade students who don't graduate in a certain year showed that, out of 50 states,

12 states had an increase in the dropout rate during the past 2 years

14 states had a dropout rate of least 30% during the past 2 years

25 states had an increase in the dropout rate and/pr a dropout rate of at least 30% during the past 2 years

A: how many states had both a dropout rate of at least 30% and an increase in the dropout rate over the 2 year period?

B: How many states had a dropout rate that was less than 30% but that had increased over the 2 year period?

Answer 1

Answer:

a)

Given,

Here there are total states = 50

n(A) = 12

n(B) = 14

n(A B) = 25

Now let us consider,

n(A B) = n(A) + n(B) - n(A B)

n(A B) = n(A) + n(B) - n(A B)

substitute the values given

n(A B) = 12 + 14 - 25

= 26 - 25

n(A B) = 1 state

b)

Given,

To determine the number of states that had a dropout rate that was less than 30% but that had increased over the 2 year period.

i.e.,

Only A

= n(A) - n(A B)

substitute values

= 12 - 1

= 11 states