4.2: some probability rules- compound events

(b) What is the probability of getting a sum of 11? (Enter your answer as a fraction.)

1/18

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (Enter your answer as a fraction.)

1/6

(b) What is the probability of getting a sum of 11? (Enter your answer as a fraction.)

2/9

Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy).

Add the values together

If two events A and B are independent and you know that P(A) = 0.25, what is the value of P(A | B)? (a) For mutually exclusive events, can event A occur if event B has occurred?

No. By definition, mutually exclusive events cannot occur together.

(e) Are the events N = no sale and A aggressive approach independent? Explain.

No. P(N) ≠ P(N | A).

(b) Are the events S = sale and Pa = passive approach independent? Explain.

No. P(S) ≠ P(S | Pa).

Are these outcomes mutually exclusive (for the die)

Yes

(b) Using the information from part (a), can you conclude that events A and B are not independent if they are mutually exclusive? Explain.

Yes. Because P(A|B) ≠ P(A), the events A and B are not independent.

Are these outcomes mutually exclusive? Why?

Yes. Choosing a green and blue M&M is not possible.

Are these outcomes mutually exclusive? Why?

Yes. Choosing a yellow and red M&M is not possible.

(b) Find P(yellow candy or red candy).

add the values together

Suppose two events A and B are mutually exclusive, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you'll see why two mutually exclusive events are not independent. What is the value of P(A|B)?

0

If two events A and B are independent and you know that P(A) = 0.25, what is the value of P(A | B)?

0.25

(e) The probability the student is female and is majoring in business.

P(A and B)

(d) The probability the student is female and is not majoring in business.

P(A and Bc)

(c) The probability a business major is female.

P(A | B)

Consider the following events for a college student selected at random. A = student is female B = student is majoring in business Translate each of the following phrases into symbols. (a) The probability the student is male or is majoring in business.

P(Ac or B)

(b) The probability a female student is majoring in business.

P(B | A)

(c) Find P(not purple candy).

subtract the value of the purple candy from 100