Exam 8: Essential Probability Rules

The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. Let's call X the number of color-blind individuals in a random sample of 8 Caucasian American males. The table gives the probability distribution for X. ? ? X 0 1 2 3 4 5 6 7 8 P(X) 0.513 0.357 0.109 0.019 0.002 0.000 0.000 0.000 0.000 What is the probability of getting at least 6 color-blind individuals in the sample?

What is the term for a variable whose value is a numerical outcome of a random phenomenon?

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse, as defined in the official psychiatric manual. Choose a young person (age 19 to 25) at random and ask, "In the past seven days, how many days did you watch television?" Call the response X for short. Here is a probability model for the response: ? ? Days X 0 1 2 3 4 5 6 7 Probability 0.04 0.03 0.06 0.08 0.09 0.08 0.05 ? What is the correct notation for "watched TV at least two days in the past week" in terms of X?

The Centers for Disease Control and Prevention receives information about the causes for HIV/AIDS infection in the United States. Here are the causes of infection and their respective probability among American women age 20 to 24 years: ? ? Injection drug use Heterosexual sex Perinatal infection Other causes ? 0.664 0.125 0.095 What is the probability that an American woman age 20 to 24 contracted HIV/AIDS either via heterosexual sex or via perinatal infection?

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What are the odds of myopia in the 18- to 24-year-old American population?

A recent nationwide study of myopia (nearsightedness) found that 38.1% of Americans age 18 to 24 suffer from myopia. What is the probability that a randomly chosen American between the ages of 18 and 24 does NOT have myopia?

The probability density of a random variable X is given in the figure. What is the probability that X = 1.5?

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, what is the probability of A or B?

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among American women age 20 to 24 is 2791.5 per 100,000. What are the approximate odds of a Chlamydia infection in the 20- to 24-year-old U.S. female population?

The probability density of a random variable X is given in the figure. What is the value of P(0 < X ≤ 2)?

Based on a recent Gallup survey, we define the following probability model for the number X of daily cups of coffee consumed by Americans. ​ ​ 0 1 2 3 4 or more Probability 0.36 0.26 0.19 0.09 ? What is the probability that an American does NOT consume 2 cups of coffee daily?

Based on data from the U.S. Department of Agriculture, we define the following probability model for the number X of different pesticides detected in fresh produce. ​ ​ X 0 1 2 3 4 5 or more Probability 0.43 0.17 0.14 0.08 0.06 0.12 What is the numerical value for the probability P(X < 2)?

Some argue that millions of Americans are so hooked on television that their viewing habits fit the criteria for substance abuse, as defined in the official psychiatric manual. Choose a young person (age 19 to 25) at random and ask, "In the past seven days, how many days did you watch television?" Call the response X for short. Here is a probability model for the response: ? ? Days X 0 1 2 3 4 5 6 7 Probability 0.04 0.03 0.06 0.08 0.09 0.08 0.05 ? For a randomly selected student, which of the following terms describes the events X = 3 and X = 4?

Which of the following defines an event considered to have an unusual probability?

The probability density of a random variable X is given in the figure. What is the probability that X is at least 1.5?

What is the probability that an event will occur?

Studies indicate that approximately 7% of Americans are vegetarians. If an American is selected at random, what is the probability that he or she is NOT a vegetarian?

A physician observes the number of lesions on subjects who regularly used tanning salons. Let X be the number of lesions observed. The physician found that X had the following probability distribution. ? ? Value of 0 1 2 3 4 Probability 0.05 0.1 0.25 0.30 0.30 What is the probability that a randomly chosen subject has at least three lesions?