G163 Essential Statistics and Analytics and Homework

Name: Queenkleen_____

Module 03 Homework Assignment

1.) A nurse at a fertility clinic has a couple who is interested in having three children and wants to know the probability of having exactly one boy. To help the nurse determine the probability of having exactly one boy answer the following questions:

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a.) Describe the sample space in terms of B and G for a couple having three children. 

Sample spaces (G=girl and B=boy), Total outcome = =8. N= number of children. 0 boy =(GGG)= 1 outcome 1 boy = (BGG), (GBG), (GGB)= 3 outcomes 2 boys=(BBG), (BGB), (GBB)=3 outcome 3 boys=(BBB)= 1 outcomes

b.) What is the probability of having exactly one boy out of three children?

The probability of having only 1 boy= (favorable outcome)

c.) The couple decides to have three boys. What is probability of having three boys out of three children?

The probability of having 3 boys = (favorable outcome) total outcome) =1

d.) Would it be “unusually low” to have three boys? Explain.

Yes, it would be unusually low to have 3 boys because the probability of having 3 boys are much less. Some may even have 3 girls favorable.

2.) A die is rolled. Find the following probabilities:

a.) P(rolling a 5)

The total outcome of rolling a die is 1,2,3,4,5,6 which =6 Favorable outcome=number of times 5 occur=1

b.) P(rolling a 7)

Favorable outcome=number of times 7 occur=0 P=rolling a 7= favorable outcome total outcome)=0

c.) P (rolling an even number)

Favorable outcome= number of times even number=2,4,6 occurs=3 3

d.) P (rolling a number less than 5)

Favorable outcome= number of times a number less than 5 occur=1,2,3,4=4 0.67

e.) P(rolling a number less than or equal to 6)

Favorable outcome=number of times a number less or equal to 6 occur=1,2,3,4,5,6 =6

3.) In a recent survey, the following data was obtained in response to the question “When making a purchase, do you prefer to pay with cash or a credit card?” The responses are listed in the table.

Gender Cash Credit Card Total

Males 21 39 60

Females 15 25 40

Total 36 64 100

a.) What is the probability that a randomly selected person is a female or prefers to pay with cash?

P = 15+21+2561

b.) What is the probability that a randomly selected person is a male or prefers to pay with a credit card?

P (malecredit card) = 39

c.) What is the probability that a randomly selected person is a female and prefers to pay with cash?

P (female =15

d.) What is the probability that a randomly selected person is a male and prefers to pay with a credit card?

15

e.) Given that the person prefers to pay with a credit card, what is the probability that the person is a male?

P =male 390.609375 Therefore, required probability is 0.6094 (rounded to four decimal places)

f.) Given that the person is a female, what is the probability that she prefers to pay with cash?

P =male 25

4.) Your instructor administers a 5 question multiple choice test. Each question has 4 possible answers of which 1 answer is correct. Find the probability of getting at least 1 question correct.

Probability of success = 0.763

5.) You and 5 friends are interested in forming a club. How many different ways can a President, Treasurer and Secretary be selected?

5+1=6 From these 6 members I can select president, treasurer and secretary. 6P3 = 6! / (6 - 3) = 6 * 5 * 4 * 3 / 3! = 6 * 5 * 4 = 120 Therefore, there are 120 different ways are possible.

6.) A journalist has 10 books to review. Of the 10 books being reviewed, he can select 4 reviews for publication. How many ways can the 4 reviews be selected?

There are 10 books to review Of the 10 books he selects 4 reviews for publication Required ways = 10C4 = 210 ways

7.) Winning the grand prize at a carnival game requires you to randomly select 7 different numbers, ranging from 0 to 35, and matching the same 7 numbers drawn at the end of the carnival. The order in which you select the 7 numbers does not matter. What is the probability of winning the prize?

=7=6724520 16724520=0.000000149