4. Probability

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?

Given the following probability distribution, determine whether it is a discrete probability distribution: $x$: $1$, $2$, $3$; $P\left(x\right)$: $0.2$, $0.5$, $0.3$.

In probability theory, what is the main difference between an $\mathrm{outcome}$ and an $\mathrm{event}$?

Suppose the probability of getting a job interview from a single application is $p$, and you submit $n$ independent applications. Which expression gives the probability of getting at least one interview if you submit between $1$ and $10$ applications?

"[DATA] A Random Process: Green Lights On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether the light was red (1), or not (0), for 120 consecutive days in which you drove to school.

b. What proportion of the days were you stuck by a red light after 15 days?"

If the hourly wage of detasselers is normally distributed with a mean of $\backslash (13$ and a standard deviation of $\backslash )2$, what is the probability that a randomly selected detasseler makes less than $\$13$ per hour? Express your answer as $p(z<0.5)$.

Which of the following statements about the population proportion $p$ and sample proportion $p$ is correct?

Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a \$2 bet on a Justify win resulted in a winning ticket worth \$7.80.

a. How much net profit was made from a \$2 win bet on Justify?

Which of the following best describes the difference between a stratified sample and a cluster sample?

Suppose $x$ has a uniform distribution on the interval $[0,1]$. What is the probability that $x<0.25$?

Suppose $Z$ is a standard normal random variable. What is the probability that $Z<0$?

Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of \$1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect \$500, so your net profit is \$499.

c. Is there much of a difference between the actual odds against winning and the payoff odds?

Define each of the following.

d. Sample space

Notation When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P (M|B) represent? Is P (M|B) the same as P (B|M)?

In the context of probability theory, what is the probability of an event that is impossible?