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kondor19780726 [428]
2 years ago
7

The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find th

e probability of each of the events.
juniors seniors
yes 28 97
no 56 19

Express your answer as a fraction, using the backslash. Example: 17 would be written as 1/7.


a) P (a junior who did not attend prom)

b) P (did not attend prom | senior)

c) P (junior | attended prom)
Mathematics
2 answers:
vladimir2022 [97]2 years ago
4 0

Answer:

<u>A. P = 7/25 </u>

<u>B. P = 19/116</u>

<u>C. P = 28/125</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly this way:

     <u> Juniors  Seniors   Totals</u>

Yes       28         97          125

No       56         19           75

<u>Totals</u>   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

Zielflug [23.3K]2 years ago
3 0

Answer:

(a)\frac{7}{25}

(b)\frac{19}{116}

(c)\frac{28}{125}

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

  • Total of those who attended prom=125

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

  • Total of those who attended prom=75
  • Total Number of students=200

(a) P (a junior who did not attend prom)

P(J')=\frac{56}{200}= \frac{7}{25}

(b)

P(Senior)=\frac{116}{200}

P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}

(c)P (junior | attended prom)

P(Senior)=\frac{84}{200}

P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}

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