Question

Question 1: A marketing company chooses a survey participant among two respondents: one female and one male. The chosen participant is then asked to rate either product A, B, or C.

What is the probability that the respondent was male and rated product B?

Question 2: A company receives equipment from two factories: 38% from factory A, and all other equipment from factory B. Each factory has a percentage of equipment that is defective: 1% of factory A's equipment is defective, while 4% of factory B's equipment is defective.

If a piece of the company's equipment is selected at random, what is the probability that it is defective and from factory B?

These questions are twisting my brain, could someone please help me out with a step by step solution?

Answer 1

If A and B are two independent events, then P(A and B) = P(A) * P(B)

Question (1)

Given there are two respondents for the survey: one female and one male.

Probability that the respondent was male = 1/2

Probability that the respondent was female = 1/2

Given that the chosen participant is then asked to rate either product A, B, or C.

Probability that product A was rated = 1/3

Probability that product B was rated = 1/3

Probability that product C was rated = 1/3

Now we want the probability that the respondent was male and rated product B

Let event X be that the respondent was male

Let event Y be that the rated product was B

Here X and Y are independent events since happening or orccuing of X doesn't effect the happening or occuring of Y

So P(X and Y) = P(X) * P(Y)

=1/2 *1/3

= 1/6

= 0.166666

So probability that the respondent was male and rated product B = 0.166666

Question (2)

A company receives equipment from two factories: 38% from factory A, and all other equipment from factory B

Probability that the equipment is from Factory A = 0.38

Probability that the equipment is from Factory B = 0.62

Each factory has a percentage of equipment that is defective: 1% of factory A's equipment is defective, while 4% of factory B's equipment is defective.

Probability that the equipment is defective in factory A = 0.01

Probability that the equipment is defective in factory B = 0.04

If a piece of the company's equipment is selected at random, what is the probability that it is defective and from factory B

Let event X be the equipment is from Factory B

Let event Y be equipment is defective in factory B

Here X and Y are independent events since happening or orccuing of X doesn't effect the happening or occuring of Y

P( X and Y) = P(X) * P(Y)

= 0.62 * 0.04

= 0.0248

If a piece of the company's equipment is selected at random, what is the probability that it is defective and from factory B = 0.0248