1) Dunn Pontiac has compiled the following sales data regarding the number of cars sold over the past 60 selling days

1) Dunn Pontiac has compiled the following sales data regarding the number of cars sold over the past 60 selling days. Answer the

following questions for the sales data shown.

Dunn Pontiac Sales Data

Number of Cars Sold	Number of Days
0	5
1	5
2	10
3	20
4	15
5 or more	5
Total	60

Relative Frequency Probability is used:

P(E) = number of desired past observations

Total observations

a) What is the probability that two cars are sold during a particular day?

The events are mutually exclusive. If two cars are sold in a day,

four cannot be sold that day.

P(Exactly 2 cars sold) = Number of days two cars were sold

Total number of days

= 10 = 0.1667

b) What is the probability of selling 3 or more cars during a particular day?

Let X represent the number of cars sold.

P( X 3 ) = P(3) + P(4) + P(5 or more) = 20 + 15 + 5 = 40 = 0.67

60 60 60 60

c) What is the probability of selling at least one car during a particular day?

Let X represent the number of cars sold.

P( X 1 ) = P(1) + P(2) + P(3) + P(4) + P(5 or more) =

5 + 10 + 20 + 15 + 5 = 55 = 0.9166 = 0.92

60 60 60 60 60 60

A faster way using the complement rule i.e. 1 – probability of not selling any cars:

P( X 1 ) = 1 – P(0) = 1 – 5 = 1 – 0.08 = 0.92

2) A local community has two newspapers. The Morning Times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?

Note that the group that reads both papers is being counted twice.

(percentages add up beyond 100%)

Let M = those reading the Morning Times,

E = those reading the Evening Dispatch

P( M or E) = P(M) + P(E) – P(M and E)

= 0.45 + 0.60 – 0.20 = 0.85

3) Yesterday, The Bunte Auto Repair Shop received a shipment of four Carburators. One is known to be defective. If two are scheduled at random and tested:

The selection of 2 carburators are not independent events, because the selection of the first removes it from consideration by the second (selection without replacement).

a) What is the probability that neither one is defective?

Let G1 be the first "good" carburetor and G2 the second one.

P(G1 and G2) = P(G1)P(G2|G1)

32 = 6 = 0.5

4 3 12

b) What is the probability that the defective carburator is

located by testing two carburators?

This means the defective carburator is located in the first test or the second test.

Let D1 represent the defect in the first test and D2 that in the second test.

P(finding the defect) = P(G1)P(D2|G1) + P(D1)P(G2|D1)

= 3 1 + 13 = 0.5

4 3 4 3

4) A Deli bar offers a special sandwich for which there is a choice

of five different cheeses, four different meat selections, and three different rolls. How many different sandwich combinations are possible?

Number of CMR = 5*4*3 = 60

5) 3 Scholarships are available for meritorious and needy students. Their values are $1,000, $1,200, and $1,500. Twelve students have applied and no student may receive more than one scholarship. Assuming the twelve students are meritorious and needy, how many different ways can the scholarships be awarded?

nPr = n! = 12! = 12*11*10*9! = 1320

(n-r)! (12-3)! 9!

Where n = total number of applicants

r = number of scholarships

6) The Basketball Coach at Dalton University is quite concerned about their 40 straight losses. (!) The frustrated coach decided to select the starting lineup for the DU-UCLA game by drawing five names from the 12 available players at random. (Assume that a player can play any position.) How many different starting lineups are possible?

nCr = n! = 12! = 12*11*10*9*8*7! = 11*2*9*4 = 792

r!(n-r)! 5!(12-5)! 5*4*3*2*1*7!

Where n = total number of available players

r = number in the starting lineup