Exam 4: Probability and Counting Rules

A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is $\frac { 1 } { 4 }$ , and the probability of selecting a blue chip on the first draw is $\frac { 5 } { 16 }$ , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.

If a coin is tossed three times, the probability that the coin lands on heads at least one of those three times is 7/8.

Below are listed the numbers of engineers in various fields by sex. Choose one engineer at random. Find $P$ (electrical|male). Mechanical Electrical Biomedical Male 9691 4997 6064 Female 2061 1015 5937

There are 2,368 possible ways that a committee of eight people can be selected from a group of 14 people.

Let $A$ and $B$ be events with $P ( A ) = 0.9 , P ( B ) = 0.4$ , and $P ( A$ and $B ) = 0.36$ . Are $A$ and $B$ independent?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the Probability (as a reduced fraction) that both answers are "C". [Hint: List all the outcomes Of the sample space first.]

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. Response Number Very satisfied 599 Somewhat satisfied 4694 Dissatisfied 7410 Total 12,703 What is the probability that a sampled person was only somewhat satisfied or dissatisfied government's spending?

A committee consist of 8 women and 11 men. Three members are chosen as officers. What is the probability that all three officers are women?

In a recent study, the following responses were obtained to the question, "Do you favor re in your neighborhood?" Males 25 15 10 Females 30 10 10 If a response is picked at random, what is the probability that it came from a male or that indicated no opinion regarding recycling?

There are four instructors, nine assistant professors, and five associate professors in the Math department. A committee of five is selected to choose new textbooks. There are 1,440 ways that a committee can be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.

There are 3 blue balls, 5 red balls, and 2 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one Was white?

A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done?

There are 3 first grade children, 5 second grade children, and 7 third grade children in a room. When choosing two children, what is the conditional probability of choosing a Second grade child, given that either a first or a third grade child was chosen first?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the Probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the Outcomes of the sample space first.]

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?

In a second grade class containing 12 girls and 11 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls?

According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 4 adults at random. The probability that all of them enjoy drinking beer is:

How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?

A survey asked 34,407 homeowners how many pets they owned. The results were as follc Number of Pets Number of Homeowners 0 6120 1 11,915 2 9360 3 6363 4 or more 649 Total 34,407 What is the probability that a sampled homeowner has more than 1 pet? wed:

If a card is drawn from an ordinary deck of cards, and then a second card is drawn from the same deck without replacing the first card, these two events are .