Question

2III. Two similar groups of students took equivalent math tests. Which of

the following results indicates the higher relative score?

1. A score of 60 on a test for which the mean score is 70 and s = 10.

2. A score of 480 on a test for which the mean score is 500 and s = 50.

IV. a. A fair coin is tossed 5 times. What is the probability that the sequence of tosses is HTHTT?

b.A fair die is rolled three times. What is the probability that all three rolls are 6?

c.A fair coin is tossed four times. What is the probability that it comes up heads at least once?

V. a. Let A and B be events with P(A) = 0.4 and P(B) = 0.8. Assume that A and B are independent. Find P(A and B).

b.Let A and B be events with P(A) = 0.7, P(B) = 0.1, and P(B/A) = 0.2. Find P(A and B).

VI. A certain ice cream parlor offers 16 flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.

a.In how many ways can you choose a cone is it matters which flavor is on top, which is in the middle, and which is on the bottom?

b.In how many ways can you choose a cone if the order of the flavors doesn’t matter?

2 III. Two similar groups of students took equivalent math tests. Which of the following results indicates the higher relative score? A score of 60 on a test for which the mean score is 70 and s = 10. b. A score of 480 on a test for which the mean score is 500 and s = 50. IV. a. A fair coin is tossed 5 times. What is the probability that the sequence of tosses is HTHTT? b.A fair die is rolled three times. What is the probability that all three rolls are 6? c.A fair coin is tossed four times. What is the probability that it comes up heads at least once? V. a. Let A and B be events with P(A) = 0.4 and P(B) = 0.8. Assume that A and B are independent. Find P(A and B). b.Let A and B be events with P(A) = 0.7, P(B) = 0.1, and P(B/A) = 0.2. Find P(A and B). VI. A certain ice cream parlor offers 16 flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors. a. In how many ways can you choose a cone is it matters which flavor is on top, which is in the middle, and which is on the bottom? b.In how many ways can you choose a cone if the order of the flavors doesn't matter?

Answer 1

III)

We will compare z score for a,b so that we can decide which is better

z=(X-u)/s

a ) Given score X=60

Mean u =70

Standard deviation s= 10

z1=(60-70)/10=-1

b) Given score X =480

Mean u= 500

Standard deviation s= 50

z2=(480-500)/50=-0.4

Since z2>z1

a is relatively higher than b

IV)

a)

No. Of possible elements in sample space for coin tossing 5 times is (1/2)^5=1/32

We need one possible case in 32 cases

Therefore probability for HTHTT =1/32

b)

A fair die is rolled 3 times

Total no. Of possible case for die rolling 3 times is 216

We can get only one way for getting 3 6's in 3 rolls

Therefore probability of getting 3 6's in 3 rolls is 1/216

c)

Probability of getting atleast one head can be calculated by = 1-pr( getting head 0 times)

Pr(getting head for 0 times ) =1/16

V)

a)

P(A)=0.4

P(B)=0.8

P(A and B) = P(A)*P(B) ( this is formaula for independent events )

P(A and B)= 0.4*0.8=0.32

b)

P(A)=0.7

P(B)=0.1

P(B/A)=0.2

P(A and B)=P(B/A)*P(A)=0.2*0.7=0.14

VI)

a) choosing 3 flavours from 16 can be done in 16C3 ways where order is not important

16C3=16!/(13!*3!)= 560

Therefore choosing 3 flavours from 16 where order is not important is 560 ways

b) arranging 3 flavours from 16 can be done in 16P3 ways

16P3=16!/13!=3360

Therefore arranging 3 flavours from 16 where order important is 3360 ways