Hawkes Learning Business Statistics 4.3

You are using a local home remodeling company to remodel your kitchen. They have 15 different cabinet door styles, 12 counter top choices, and 13 different types of flooring. How many different kitchen remodels could be done using these material choices?

15 * 12 * 13 = 2340

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 4 types of drinks to choose from, 6 types of sandwiches, and 4 types of chips. How many different value meal packages are possible?

4 * 6 * 4 = 96

Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 6 people, and there are 6 different possible weapons and 9 possible rooms. At one point in the game, you have narrowed the possibilities down to 4 people, 5 weapons, and 7 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct? Enter a fraction or round your answer to 4 decimal places, if necessary.

Step 1. 4 * 5 * 7 = 140 Step 2. 1/140

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a jack and then, without replacement, a face card? Express your answer as a fraction or a decimal number rounded to four decimal places.

Step 1. Use the multiplication rule for dependent events since the cards are drawn without replacement. Recall that a standard deck of 52 cards has 4 jacks. Let E be the event "drawing a jack". Therefore, P(E) will be P(E) = 1/13 Step 2. Since a jack was already drawn, we are left with 51 cards to choose from. Let F be the event "drawing a face card". Therefore, P(F|E) will be P(F|E) = 11/51 Step 3. From the past two steps we know that P(E)=4/52 and P(F|E)=11/51. Therefore, using the multiplication rule for dependent events we will have P(E and F) = P(E) * P(F|E) = 4/52 * 11/51 = 11/663 or .0166

Ashley's Internet service is terribly unreliable. In fact, on any given day, there is a 70% chance that her Internet connection will be lost at some point that day. What is the probability that her Internet service is not broken for six days in a row? Enter a fraction or round your answer to 4 decimal places, if necessary.

.3 * .3 * .3 * .3 * .3 *.3 = .0007

There are 30 different colored pencils in a box. What is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement? Enter a fraction or round your answer to 4 decimal places, if necessary.

1/30 * 1/29 = 1/870

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 10 Pennies 7 Dimes 18 Nickels 27 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime? Express your answer as a fraction or a decimal number rounded to four decimal places.

10/62 * 7/61 = 70/3782 or .0185

Mrs. Burke's mathematics class has 105 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday's work. (Mathematics Major = MM, Non-Mathematics Major = NMM) Academic Year: - Freshman = MM 12 , NMM 14 - Sophomore = MM 11, NMM 13 - Junior = MM 12, NMM 15 - Senior = MM 15, NMM 13 Step 1 of 2 : What is the probability that she selects a non-mathematics major, given that she chooses randomly from only the sophomores? Enter a fraction or round your answer to 4 decimal places, if necessary.

13/24

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a spade for the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.

13/51

Step 2 of 2 : What is the probability that she selects a sophomore, given that she chooses a non-mathematics major? Enter a fraction or round your answer to 4 decimal places, if necessary.

14 + 13 + 15 + 13 = 13/55

Out of 419 applicants for a job, 158 have over 5 years of experience and 63 have over 5 years of experience and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience? Enter a fraction or round your answer to 4 decimal places, if necessary.

63/158

Step 2 of 2 : Consider that 82 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 5 years of experience, given that the applicant has a graduate degree? Enter a fraction or round your answer to 4 decimal places, if necessary.

63/82

A box contains 10 green marbles and 8 white marbles. If the first marble chosen was a green marble, what is the probability of choosing, without replacement, a white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.

8/17

Determine if the following events are independent. Going to the gym. Losing weight.

Dependent

On a four-day vacation, the forecast is a 55% chance of rain every day. What's the probability that it rains every day? Enter a fraction or round your answer to 4 decimal places, if necessary.

Step 1. First, find the probability that it rains on one particular day of the vacation. 55% = .55 Step 2. Hence, the probability that it rains on any day of the vacation is 0.55.We assume that the weather on any given day is not affected by the weather on the other days, so the events of raining on two separate days are independent. Thus, use the extended Multiplication Rule for Probability of Independent Events to find the probability that it rains on all four days of the vacation. Enter a fraction or round your answer to 4 decimal places, if necessary. .55 * .55 * .55* .55 = .0915