Question

A physics class has 50 students. Of​ these, 10 students are physics majors and 12 students are female. Of the physics​ majors, three are female. Find the probability that a randomly selected student is female or a physics major.

Answer 1

Answer:

38% probability that a randomly selected student is female or a physics major.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Physics majors or female

10 physics majors(of which 3 are female).

12 female(the 3 female physics majors have already been counted, so we count 9)

$D = 10 + 9 = 19$

Total outcomes:

50 students, so $T = 50$

Probability

$p = \frac{D}{T} = \frac{19}{50} = 0.38$

38% probability that a randomly selected student is female or a physics major.

Answer 2

Answer:

$P(F) = \frac{12}{50}$

$P(P)= \frac{10}{50}$

$P(P \cap F) = \frac{3}{50}$

And we are interested on this probbaility:

$P(F \cup P)$

And we can use the total rule of probability and we got:

$P(F \cup P) =P(F) -P(P) -P(F \cap P)= \frac{12}{50} +\frac{10}{50} -\frac{3}{50} = \frac{19}{50}$

Step-by-step explanation:

For this case we know that the total sample is n =50

10 students are physics majors

12 students are female.

Of the physics​ majors, three are female

So we can define the following events:

P = the person selected is a physics mayor

F= the person selected is female

And we can calculate the following probabilities:

$P(F) = \frac{12}{50}$

$P(P)= \frac{10}{50}$

$P(P \cap F) = \frac{3}{50}$

And we are interested on this probbaility:

$P(F \cup P)$

And we can use the total rule of probability and we got:

$P(F \cup P) =P(F) -P(P) -P(F \cap P)= \frac{12}{50} +\frac{10}{50} -\frac{3}{50} = \frac{19}{50}$