Quiz 4

1. If a person draws a playing card and checks itssuit and then spins a three-space spinner, describe the sample space of possible outcomes using C, D, H, S for the  card outcomes and 1, 2, 3,  for the  spinner outcomes.

The sample space is S = __________________–

2.  The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts​ (a) through​ (e).

​(a) Is the given table a probability​ model? Why or why​ not?

1. No; the sum of the probabilities of all outcomes does not equal 1.
2. ​No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to​ 1, and the sum of the probabilities of all outcomes does not equal 1.
3. ​No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1.
4. ​Yes; the rules required for a probability model are both met.

(b)  What is the probability that a randomly selected murder resulted from a rifle or​ shotgun?
​P(rifle or ​shotgun) = ______ ​(Type a decimal rounded to three decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice.

1. If 1000 murders were randomly​ selected, exactly ____ of them would have resulted from a rifle or shotgun.
2. If 1000 murders were randomly​ selected, we would expect about ___  of them to have resulted from a rifle or shotgun.

(c)  What is the probability that a randomly selected murder resulted from a​ handgun, rifle, or​ shotgun?
​P(handgun, rifle, or ​shotgun) = ____ ​(Type a decimal rounded to three decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice.

1. If 1000 murders were randomly​ selected, exactly ____ of them would have resulted from a​ handgun, rifle, or shotgun.
2. If 1000 murders were randomly​ selected, we would expect about ____ of them to have resulted from a​ handgun, rifle, or shotgun.

​(e)  Are murders with a shotgun​ unusual?

1. No
2. Yes

3.   Explain the Law of Large Numbers. How does this law apply to gambling​ casinos?  Choose the correct answer below.

1. As the number of repetitions of a probability experiment​ increases, the proportion with which a certain outcome is observed gets closer to 1. This applies to casinos because they are able to make a profit in the long run because they have a small statistical advantage in each game.
2. As the number of repetitions of a probability experiment​ increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. This applies to casinos because they are able to make a profit in the long run because they have a small statistical advantage in each game.
3. As the number of repetitions of a probability experiment​ increases, the proportion with which a certain outcome is observed gets closer to 0. Casinos use the Law of Large Numbers to determine how many players gamble in certain games.
4. As the number of repetitions of a probability experiment​ increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. Casinos use the Law of Large Numbers to determine how many players gamble in certain games.

4. In a national survey college students were​ asked, “How often do you wear a seat belt when riding in a car driven by someone​ else?” The response frequencies appear in the table to the right.​ (a) Construct a probability model for​ seat-belt use by a passenger.​ (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else?

​(a) Complete the table below.

​(b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else?

1. ​No, because the probability of an unusual event is 0.
2. Yes, because 0.01 < ​P(never) < 0.10.
3. ​No, because there were 145  people in the survey who said they never wear their seat belt.
4. ​Yes, because ​P(never) < 0.05.

5.  In a recent​ survey, it was found that the median income of families in country A was ​$57,800. What is the probability that a randomly selected family has an income greater than ​$57,800?
What is the probability that a randomly selected family has an income greater  than $57,800​? ____

6.  Determine whether the probabilities below are computed using the classical​ method, empirical​ method, or subjective method. Complete parts ​(a) through ​(d) below.

​(a) The probability of having  girls in an ​-child family is 0.015625.

1. Subjective method
2. Empirical method
3. Classical method
4. It is impossible to determine which method is used.

(b) On the basis of a survey of 1000 families with six ​children, the probability of a family having six girls is 0.0059.

1. Empirical method
2. Subjective method
3. Classical method
4. It is impossible to determine which method is used.

​(c) According to a sports​ analyst, the probability that a football team will win the next game is 0.39.

1. Classical method
2. Subjective method
3. Empirical method
4. It is impossible to determine which method is used.

​(d) On the basis of clinical​ trials, the probability of efficacy of a new drug is 0.78.

1. Subjective method
2. Empirical method
3. Classical method
4. It is impossible to determine which method is used.

7.  A standard deck of cards contains 52 cards. One card is selected from the deck.

(a) Compute the probability of randomly selecting a club or diamond.
​(b) Compute the probability of randomly selecting a club  or  diamond or spade.
​(c) Compute the probability of randomly selecting a thee  or diamond.
​

(a)​ P( club or diamond​) = _____ ​(Type an integer or a decimal rounded to three decimal places as​ needed.)
​(b)​ P( club or  diamond or spade​) = ____ ​(Type an integer or a decimal rounded to three decimal places as​ needed.)
​(c)​ P( three or diamond​) = ____ (Type an integer or a decimal rounded to three decimal places as​ needed.)

8.   Find the probability of the indicated event if ​P(E) = 0.40 and ​P(F) = 0.35.
Find​ P(E or​ F) if​ P(E and ​F) = 0.05.

​P(E or ​F) = ____ ​(Simplify your​ answer.)

9.  A survey of  200 randomly selected high school students determined that  17 play organized sports. 
​(a) What is the probability that a randomly selected high school student plays organized​ sports?
​(b) Interpret this probability.

​(a) The probability that a randomly selected high school student plays organized sports is ____ ​(Round to the nearest thousandth as​ needed.)

​(b) Choose the correct answer below. ​(Type a whole​ number.)

1. If​ 1,000 high school students were​ sampled, it would be expected that about ___ of them play organized sports.
2. If​ 1,000 high school students were​ sampled, it would be expected that exactly ____ of them play organized sports.