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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 being either a freshman or junior?
0.50
0.07
0.44
0.25

Sagot :

Answer:

0.50 :)

Step-by-step explanation:

The probability of the union of being either a freshman or junior is 0.50

What is probability?

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

Formula of the probability of an event A is:

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes,

n(S) is the total number of events in the sample space.

For given example,

Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

⇒ P(freshman) = 0.25

⇒ P(sophomores) = 0.25

⇒ P(juniors) = 0.25

⇒ P(seniors) = 0.25

We know for event A and B,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Assuming event A : student is a freshman

event B : student is junior

P(A) = 0.25

P(B) = 0.25

The number of students who are freshman as well as junior = 0

⇒ n(A ∩ B) = 0

⇒ P(A ∩ B) = 0

Now, the probability of the union of being either a freshman or junior would be,

⇒ P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A ∪ B) = 0.25 + 0.25 - 0

⇒ P(A ∪ B) = 0.50

Therefore, the probability of the union of being either a freshman or junior is 0.50

Learn more about probability here:

brainly.com/question/11234923

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