Question

Each person in a group of college students was identified by graduating year and asked when he or she preferred taking classes: morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred morning classes given he or she is a junior. Round to the nearest thousandth. Survey of Class Times Freshman Sophomore Junior Senior Morning 20 14 16 17 Afternoon 5 10 2 7 Evening 15 15 8 14

Answer 1

0.615

Explanation:

The frequency table is attached below.

We have to calculate, the probability that the student preferred morning classes given he or she is a junior.

i.e
`P(\text{Morning }|\text{ Junior})`

We know that,

`P(A\ |\ B)=(P(A\ \cap\ B))/(P(B))`

So,

`P(\text{Morning }|\text{ Junior})=\frac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}`

Putting the values from the table,

`\frac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}=((16)/(143))/((26)/(143))=(16)/(26)=0.615`