Please show all details so I can understand the process I dr

Please show all details so I can understand the process. I drew a venn diagram and attempted to formally write P( )= but not so sure I have done it correctly.

Question:

A class of 50 students, each with multiple majors has 25 in Math and Physics, 20 in Physics and Chem, 15 in Math and Chem, and 5 in Math, Physics and Chem.

a. Find the probability that a randomly selected student is both a physics and chem major.

b. Find the probability that a randomly selected student is both a physics and chem major, but not a math major.

c. Find the probability that a randomly selected student is a physics major.

Thank you.

Solution

A.

There are 20 Physics and chem majors out of 50.

Hence,

P(P and C) = 20/50 = 0.40 [ANSWER]

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B.

N(P and C and not M) = N(P and C) - P(M and P and C)

= 20 - 5 = 15

Thus, 15 out of 50 are both a physics and chem major, but not a math major.

Thus,

P(P and C and not M) = 15/50 = 0.30 [ANSWER]

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C.

N(P) = N(P and M) +N(P and C) - N(M and P and C)

= (25 - 5) + (20 - 5) + 5

= 40

Thus,

P(Physics) = 40/40 = 0.80 [ANSWER]