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const2013 [10]
3 years ago
15

At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.15. The

probability that a student is a senior and plays a sport is 0.10. What is the probability that a randomly selected student plays a sport, given that the student is senior?
A. 0.10
B. 0.15
C. 0.66
D. 0.40

Please explain
Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Use the definition of conditional probability:

P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}

We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so

P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40

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Step-by-step explanation:

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Start by simplifying the "left hand side of the equation:

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Now, rewrite the equation:

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   \frac{9}{7}x =9 ;    Solve for "x" ;

We now multiply each side of the equation by "7" ;

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  on the "left-hand side" of the equation:

  7 *\frac{9}{7}x = 9 * 7  ;

On the "left-hand side" of the equation:

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On the "right-hand side" on the equation; we find that: "9 * 7 = 63 ."

   So; we can rewrite the equation:

          9x = 63 ;

To solve for "x" ; we divide each side of the equation by:  "9" ;

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Hope this answer—and explanation—is helpful!

  Best wishes to you!

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