## Statistics for Data Analysis

Probability Assignment

Submit your answers in a word document. Please show the question number and answers clearly shown. Ensure your name is in the document and that it is part of the word document name.

Feel free to add comments describing your line of thinking if you think it is appropriate.

Q1. If a single die is thrown, calculate the following probabilities for the value of X, where X is the value of the die. Show your answers in ratio format “2/20” and decimal format “0.1”

a) P (X=1)

b) P (X=7)

c) P (X=6)

d) P (X>5)

e) P (X is odd)

f) P (X <= to 5)

Q2. If 2 dice are thrown, calculate the following probabilities for the value of X, where X is the sum of the 2 dice. Show your answers in BOTH ratio format “2/20” and decimal format “0.1”

a) P (X=3)

b) P (X>10)

c) P (X<=4)

d) P (X>=7)

e) P (X is even)

f) P (X is > 10 and <=20)

Q3. The following information is obtained from a survey about liking coffee and tea as a beverage.

A total of 110 people were surveyed Show your answers in ratio format and decimal format.

Response Numbers

Likes Coffee 80

Likes Tea 70

Based on this sample, calculate the following probabilities

a) A person likes coffee or they like tea

Hint:

P (A U B) = P (A) + P (B) – P (A ∩ B)

b) A person does not like coffee or they do not like tea

c) A person likes coffee and they like tea

Hint:

P (A ∩ B) = P (A) * P (B)

d) A person does not like coffee and they do not like tea

Q4. What is the conditional probability that a person from the previous question likes tea given that they do not like coffee? Show your answers in ratio and decimal formats.

Hint:

P (A|B) = P (A ∩ B) / P (B)

Q5. If you tossed 3 fair dice, how many possible outcomes are there for their sum?

Q6. If you tossed 5 fair coins, how many possible outcomes are there?

Q7. A bag of cookies has 10 chocolate and 20 vanilla. You take out a cookie and give it to your friend. You then take out a second cookie for yourself. Calculate the following probabilities. Show your results in ratio and decimal formats.

a) P (A) where A is the event where the first cookie is chocolate

b) P (B) where B is the event where the second cookie is also chocolate

Q8. Assume a 4 digit ATM pin number can have a digit from 1 to 9

The same digit cannot be used more than one time

What is the probability that the PIN includes a “3” as one of the digits.

Hint

Use the combination formula (because order does not matter) shown on the class slides. Determine how many possible outcomes there are for a choosing 4 digits from 9 possible digits with no replacement, ie each digit cannot be reused from the 9 possible digits. The numerator would be based on the combination formula for 4 choose 1. Four digits in the PIN are used to select a single value, ie 3. Remember probability is the ratio of the number of successes to the total possible number of outcomes.

Q9. There are 10 people at a meeting and a 5 person committee is randomly selected from those attending. What is the probability that a specific person, ie John Smith will be on the committee? Remember probability is the ratio of the number of successes to the total possible number of outcomes.

Hint

Use the combination formula shown on the class slides to determine how many possible combinations there are for randomly choosing 5 people from a group of 10. This will be the denominator for the probability. Consider the numerator to be how many combinations there are there for John Smith to be selected. This will make the numerator to be the combination formula of 5 choose 1. Refer to the slide called “Combinations” in the class slide deck for the formula.