Question

The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2890 21-24 2190 25-28 1276 29-32 651 33-36 274 37-40 117 Over 40 185 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 32 B = event the student is at least 37 Are the events A and B disjoint? No Yes

Answer 1

Answer:

Are the events A and B disjoint? Yes

Step-by-step explanation:

Disjoint events are those events that cannot occur at the same time, i.e. for events X and Y to be disjoint, $P(X\cap Y)=0$.

The event A is defined as the number of students whose age is at most 32.

And event B is defined as the number of students whose age is at least 37.

The events A and B are disjoint events.

• The sample space for event A consists of all the students of age group (under 21), (21 - 24), (25 - 28) and (29 - 32).

• Whereas the sample space for event B consists of all the students of age group (33 - 36), (37 - 40) and (Over 40).

The sample space for the intersection of these two events is:

Sample space of (A ∩ B) = 0

As there are no common terms in both the sample.

Hence proved, events A and B are disjoint.