Chapter 5 Probability Review

An essay test has 10 questions. Students are required to answer 7 of the 10 questions. How many different sets of questions could be answered?

10C7=120

A man is planning for college and takes a standardized test. While registering for the test, he is allowed to select two schools in which his scores will be sent to at no cost. If there are 11 colleges he's considering, how many different ways could he fill out the score report form?

11C2=55

You play a game in which you win $10 if a sum of seven results from rolling two fair dice. You win $5 if you roll doubles. Otherwise, you win nothing. In a single roll of the dice, what is the probability that you will win at least some money? Clearly communicate your reasoning and report your answer as a simplified fraction.

12/36=1/3 because How many of these are doubles or sum of 7? 12 There is a total of 36 rolls

In how many ways can a committee of three men and four women be formed from a group of 12 men and 12 women?

12C3=220 and 12C4=495 then multiply to 108,900

Math club needs to choose a president, vice president and secretary for next year. There are currently 12 members in math club. How many different presidencies are there?

12P3=1,320

A local area network requires characters for a password. The first character must be a letter, but the remaining 7 can either be a letter or a digit (0 through 9). Lower- and uppercase letters are considered the same. How many passwords are possible for the local area network?

26x36^7 The answer is too large so leave it as is.

If a new car has 2 transmission types, 3 vehicles styles, 2 option packages, 8 exterior color choices, and 2 interior color choices, how many different new cars are possible?

2x3x2x8x2=192

In a survey of 500 randomly selected people, it was determined that 22 play soccer. What is the probability that a randomly select person does NOT play soccer?

478/500=0.956

Event A has a probability of 0.5 and Event B has a probability of 0.4. If A and B are independent events, what is the probability that either A or B (or both) occur(s)? Report your answer in decimal format.

P(A and B)=0.5x0.4=0.2 P(A or B)=0.5+0.4-0.2-0.7

During the 2014 season, the Dodgers won 58% of their games. Assuming that the outcomes of the games are interdependent, and the percentage of wins will be the same as in 2014. What is the probability the Dodgers will lose at least one of their next seven games?

P(don't lose any or win all 7)=.58^7=0.0221 P(lose at least 1)=1-P(win all 7)=1-0.0221=0.978

Jaclyn plays a game of chance. Each play is independent. Each time that she plays, the probability that she wins is 0.3. She plays 3 times. What is the probability that she will win exactly 2 times? Report your result to three decimal places.

P(lose)=1-0.3=0.7 p(exactly 2 wins)=(0.3)^2x0.4x3=0.189

In 2013, there were 32,719 traffic fatalities in the US. Of these,10,076 were alcohol related. What is the probability that neither of two randomly selected traffic fatalities were alcohol related?

P(not alcohol related)=1-10076/32719=0.692 0.692^2=0.479

According to government statistics department, 20.7% of women aged 25 years or older have a Bachelor's Degree; 17.1% of women aged 25 years or older have never married; among women 25 years or older who have never married, 23.7% have a Bachelor's Degree and among women 25 years or older who have a Bachelor's Degree, 19.6% have never been married. Are the events "have a Bachelor's Degree" and "never married" independent? Explain.

The probability of "have a Bachelor's Degree" is affected by the occurrent of "never married" and vice versa (different conditional probabilities), so the events are NOT independent or dependent.

A bag of 30 tulips purchased from Glover nursey contains 12 red, 10 yellow, and 8 purple: a. What is the probability that two randomly selected bulbs are both red? b. What is the probability the first is red and the second one is yellow?

a. 12/30x11/29=0.152 b. 12/30x10/29=0.138

Let the sample space S={1,2,3,4,5,6,7,8,9,10}. Suppose the outcomes are equally likely. a. Compute the probability of selecting an even number. b. Compute the probability of selecting a number less than 3. c. Are these events disjoint?

a. 5/10=0.5 b. 2/10=0.2 c. No because 2 is an even number that is also less than 3

List all the permutations of the three options x, y, and z taken two at a time without repetition. Show this is equivalent to 3 permute 2.

xy, xz, yx, yz, zx, zy and 3P2=6 so there are 6 possible outcomes in the list