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Murrr4er [49]
3 years ago
13

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 24 of them play baseball. There are 3 students who pl

ay neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Answer:

\frac{5}{29}

Step-by-step explanation:

Let n(A) represent students playing basketball, n(B) represent students playing baseball.

Then, n(A)=7, n(B)=24

Let n(S) be the total number of students. So, n(S)=29.

Now,

P(A)=\frac{n(A)}{n(S)}=\frac{7}{29}

P(B)=\frac{n(B)}{n(S)}=\frac{24}{29}

3 students play neither of the sport. So, students playing either of the two sports is given as:

n(A\cup B)=n(S)-3\\n(A\cup B)=29-3=26

∴ P(A\cup B)=\frac{n(A\cup B)}{n(S)}=\frac{26}{29}

From the probability addition theorem,

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Where, P(A\cap B) is the probability that a student chosen randomly from the class plays both basketball and baseball.

Plug in all the values and solve for P(A\cap B) . This gives,

\frac{26}{29}=\frac{7}{29}+\frac{24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{7+24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{31}{29}+P(A\cap B)\\\\P(A\cap B=\frac{31}{29}-\frac{26}{29}\\\\P(A\cap B=\frac{31-26}{29}=\frac{5}{29}

Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is \frac{5}{29}

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