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3. The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?

a. 1. 15

b. 0. 61

c. 0. 91

d. 0. 24

Sagot :

The probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

What is condition probability?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The conditional probability is the happening of an event, when the probability of occurring of other event is given. The probability of event A, given that the event B is occurred.

Students of high school who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. In this,

  • 74% likely to tryout for softball;
  • 27% likely to tryout for volleyball;
  • 42% likely to tryout for tennis;  
  • 88% likely to tryout for swimming.

Let the tryout for volleyball is event A and tryout for swimming is event B. Thus,

P(A)=0.27

P(B)=0.88

Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

Thus, probability of the union of trying out for either volleyball or swimming

P(A or B)=P(A)+P(B)-P(A and B)

P(A or B)=0.27+0.88-P(A)*P(B)

P(A or B)=0.27+0.88-0.27×0.88

P(A or B)=0.9

Hence, the probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

Learn more about the probability here;

https://brainly.com/question/24756209

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