Included with each section or problem are reference examples and end of section exercises that can be used as a guide. Be sure to show your work so that partial credit may be awarded. To receive full credit, work must be shown if applicable.

Section 3.1: Basic Concepts of Probability and Counting

1. Lock combinations are made using 3 digits followed by 2 letters. How many different lock combinations can be made if repetition of digits is allowed? (References: example 4 page 135, end of section exercises 13 - 16 page 142 and 35 – 36 page 144) (6 points)

Answer

Three digits are given with a 2 letters. The total number of objects is 5. The repetition of digits is allowed. Hence the total number of permutation of digits is, 53 = 125

The repetitions of letters is not allowed,

Therefore 2 letters can be permutated as, [pic]

Hence the total number of lock combinations is, 125*20 = 2500.

2. In 2001 the stock market took some big swings up and down. One thousand investors were asked how often they tracked their investments. The table below shows their responses. What is the probability that an investor tracks the portfolio weekly? (References: example 6 page 137, end of section exercises 45 - 48 page 145) (5 points)

|How often tracked? |Response | |Daily |235 | |Weekly |278 | |Monthly |292 | |Few times a year |136 | |Do not track | 59 |

Answer

We have given that,

|How often tracked? |Response |

|Daily |235 |

|Weekly |278 |

|Monthly |292 |

|Few times a year |136 |

|Do not track |59 |

|Total |1000 |

By using definition of probability,

The probability that an investor tracks the portfolio weekly is,

[pic]

Hence the probability that an investor tracks the portfolio weekly is, 0.278.

Section 3.2: Conditional Probability and the Multiplication Rule

3.

a. In a battleground state, 60% of all voters are Republicans. Assuming that there are only two parties - Democrat and Republican, if two voters are randomly selected for a telephone survey, what is the probability that they one is a Republican followed by a Democrat? Round your answer to 4 decimal places. (References: example 4 page 152, end of section exercises 19 – 21 page 156 - 157) (2 points)

Answer

We have given that,

Probability of voters is Republicans is (p) 0.6

Probability of voters is Democratic is (q) 0.4

The probability that the that they one is a Republican followed by a Democrat from a two randomly selected voters is,

= 0.6*0.4 (By using multiplication rule)

= 0.2400

b. You are dealt 2 cards from a shuffled deck of 52 cards and the first card drawn is put back in the deck before the second card is drawn. What is the probability that the first card is a King and the second card is a King? Round your answer to 3 decimal places. (References: example 3 page 151. (2 points)

Answer

The number of ways of selection of 2 cards from 52 cards is,

[pic]

The number of king cards in a pack of 52 cards are, 4

The number of ways of getting a king card is, [pic]

Hence the probability of getting first card is a King and the second card is a King is,

[pic]

Hence the probability of getting first card is a King and the second card is a King is, 0.012.

4. The table below shows the drink preferences for people in 3 different age groups. If one...