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A study of 500 college students was conducted to determine the number of freshman and sophmore students who are taking a math
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A study of 500 college students was conducted to determine the number of freshman and Sophmore students who are taking math class in coming fall semester.

Taking math in fall Not Taking math in fall Total
Freshman 130 110 240
Sophmore 135 125 260
Total 265 235 500

Probability table based on above information

Probability Taking math in fall Not Taking math in fall P(X)
Freshman 0.26 0.22 0.48
Sophmore 0.27 0.25 0.52
P(Y) 0.53 0.47 1

(a) Probability that a randomly students is Sophmore given that they are taking math in the fall is P(Saphmore/Math)=\frac{P(Saphmore, Math)}{P(Math)}=\frac{0.27}{0.53}=0.5094

Answer D. 0.509

(b) Probability that a randomly students is Sophmore and is taking math in the fall is

P(Saphmore, Math)=0.27

Answer D. 0.270

(c) Probability that a randomly students is Sophmore or they are taking math in the fall is

P(Saphmore or Math)=P(Saphmore)+P(Math)-P(Saphmore, Math)=0.52+0.53-0.27=0.78

Answer C. 0.780

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