Question

1.According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)

a. Compute the probability that a randomly selected peanut M&M is not orange.

b. Compute the probability that a randomly selected peanut M&M is red or blue.

c. Compute the probability that three randomly selected peanut M&M’s are all brown.

d. If you randomly select three peanut M&M’s, compute that probability that none of them are orange.

e. If you randomly select three peanut M&M’s, compute that probability that at least one of them is orange.

2. You toss a fair coin 4 times. What is the probability that (round to 4 decimal places)

a) you get all Heads?

b) you get at least one Tail?

3. Suppose that 59% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?

Give your answer as a decimal rounded to 4 places.

4. Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 23 of the 54 boxes on the shelf have the secret decoder ring. The other 31 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?

(Give answer as a decimal correct to four decimal places.)

5. a. A bag contains 9 yellow marbles, 3 green marbles, and 7 white marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a yellow marble and then a white marble?
  

b. A bag contains 3 black marbles, 7 white marbles, and 9 green marbles. If two different marbles are drawn from the bag , what is the probability of drawing first a black marble and then a green marble?

6. Giving a test to a group of students, the grades and gender are summarized below

Grades and Gender
	A	B	C	Total
Male	19	13	12	44
Female	15	18	7	40
Total	34	31	19	84

If one student is chosen at random, find the probability that the student was male AND got a "B". Round your answer to 4 decimal places. _____

7. Giving a test to a group of students, the grades and gender are summarized below

Grades and Gender
	A	B	C	Total
Male	11	16	12	39
Female	19	7	4	30
Total	30	23	16	69

If one student is chosen at random, find the probability that the student was male OR got an "A". Round your answer to 4 decimal places. ______

8. Giving a test to a group of students, the grades and gender are summarized below. Round your answers to 4 decimal places.

Grades and Gender
	A	B	C	Total
Male	17	8	16	41
Female	10	15	11	36
Total	27	23	27	77

If one student is chosen at random,

a. Find the probability that the student was male: ____

b. Find the probability that the student was male AND got an "A": ____

c. Find the probability that the student was female OR got a "C": ____

d. If one student is chosen at random, find the probability that the student got a 'A' GIVEN they are female: _____

9. A CBS News poll involved a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

	better	same	worse
Republican	38	104	44
Democrat	12	87	137
none	21	90	118

If we randomly select one of the adults who participated in this study, compute: (round to four decimal places)

a.P(Democrat) =

b.P(worse) =

c.P(worse|Democrat) =

d.P(Democrat|worse) =

e.P(Democrat and worse) =

10. Use the following probabilities to answer the question. Round to 4 decimal places.

P(A)=0.28P(A)=0.28, P(B)=0.62P(B)=0.62, P(AandB)=0.10P(AandB)=0.10.

P(B∣A)=P(B∣A)=

11. The table summarizes results from 978 pedestrian deaths that were caused by automobile accidents.

Pedestrian Deaths
Driver Intoxicated?	Pedestrian Intoxicated?
	Yes	No
Yes	62	77
No	249	590

If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated. Please enter a decimal to 4 places. _____

12. The table summarizes results from 984 pedestrian deaths that were caused by automobile accidents.

Pedestrian Deaths
Driver Intoxicated?	Pedestrian Intoxicated?
	Yes	No
Yes	50	83
No	261	590

If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated but the driver was. Please enter a decimal to 4 places. ______

Answer 1

Solution:

Question 1)

Given: According to Masterfoods, the company that manufactures M&M’s,

12% of peanut M&M’s are brown,

15% are yellow,

12% are red,

23% are blue,

23% are orange

15% are green.

Thus we can make following table:

Color of Peanut M&M’s	Probability
Brown	0.12
Yellow	0.15
Red	0.12
Blue	0.23
Orange	0.23
Green	0.15

Part a. Compute the probability that a randomly selected peanut M&M is not orange.

P( Not Orange )= 1 - P( Orange )

P( Not Orange )= 1 - 0.23

P( Not Orange )= 0.77

Part b. Compute the probability that a randomly selected peanut M&M is red or blue.

P( Red or Blue) =.......?

Since Red and Blue are mutually exclusive events, we can write

P(Red or Blue)= P(Red) + P(Blue)

P(Red or Blue)= 0.12 + 0.23

P(Red or Blue)= 0.35

Part c. Compute the probability that three randomly selected peanut M&M’s are all brown.

P( All three are Brown) =..........?

P( All three are Brown) = 0.12³

P( All three are Brown) = 0.001728

P( All three are Brown) = 0.0017

Part d. If you randomly select three peanut M&M’s, compute that probability that none of them are orange.

P( None of them are Orange ) =..........?

P( None of them are Orange ) = ( 1 - p)³

P( None of them are Orange ) = ( 1 - 0.23)³

P( None of them are Orange ) = 0.77³

P( None of them are Orange ) = 0.4565

Part e. If you randomly select three peanut M&M’s, compute that probability that at least one of them is orange.

P( At least one of them is Orange) = .....?

P( At least one of them is Orange) = 1 - P( None of them are orange )

P( At least one of them is Orange) = 1 - 0.4565

P( At least one of them is Orange) = 0.5435