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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

Respuesta :

InesWalston

Answer:

0.615

Step-by-step 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 [tex]P(\text{Morning }|\text{ Junior})[/tex]

We know that,

[tex]P(A\ |\ B)=\dfrac{P(A\ \cap\ B)}{P(B)}[/tex]

So,

[tex]P(\text{Morning }|\text{ Junior})=\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}[/tex]

Putting the values from the table,

[tex]\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}=\dfrac{\frac{16}{143}}{\frac{26}{143}}=\dfrac{16}{26}=0.615[/tex]

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mickymike92

The probability that the student preferred morning classes given he or she is a junior is 0.615.

What is probability?

Probability is the likelihood of an event happening.

  • Probability = number of expected event/number of possible events

The probability that the student preferred morning classes given he or she is a junior is given below as:

[tex]P(\text{Morning }|\text{ Junior})[/tex]

[tex]P(\text{Morning }|\text{ Junior})=\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})} \\ [/tex]

Substituting the values from the table;

[tex]P(\text{Morning }|\text{ Junior}) = \dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}=\dfrac{\frac{16}{143}}{\frac{26}{143}}=\dfrac{16}{26}=0.615 \\ [/tex]

Therefore, the probability that the student preferred morning classes given he or she is a junior is 0.615.

Learn more about probability at: https://brainly.com/question/24756209

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