Prob & Stats Chap 5.1 HW

According to a certain​ country's department of​ education, 41.6​% of​ 3-year-olds are enrolled in day care. What is the probability that a randomly selected​ 3-year-old is enrolled in day​ care?

.416

Explain the Law of Large Numbers. How does this law apply to gambling​ casinos?

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.

Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11, 12. Because there are 11​ outcomes, he​ reasoned, the probability of rolling a nine must be 1/11. What is wrong with​ Bob's reasoning?

The experiment does not have equally likely outcomes.

Is the following a probability​ model? What do we call the outcome ​"red​"? Is the table about an example of a probability model? Color Probability red 0 green 0.35 blue 0.1 brown 0.2 yellow 0.1 orange 0.25 What do we call the outcome ​"red​"?

Yes, because the probabilities sum to 1 and they are all greater than or equal to 0 and less than or equal to 1. Impossible event

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 eight girls in an eight​-child family is 0.00390625. ​(b) On the basis of a survey of 1000 families with eight children, the probability of a family having eight girls is 0.0064. ​(c) According to a sports​ analyst, the probability that a football team will win the next game is 0.36. (d) On the basis of clinical​ trials, the probability of efficacy of a new drug is 0.81.

(a) Classical method (b) Empirical method (c) Subjective method (d) Empirical method

In a probability​ model, the sum of the probabilities of all outcomes must equal

1

Brad and Allison have three girls. Brad tells Allison that he would like one more child because they are due to have a boy. What do you think of​ Brad's logic?

Brad is incorrect due to the nonexistent Law of Averages. The fact that Brad and Allison had three girls in a row does not matter. The likelihood the next child will be a boy is about 0.5.

A national survey asked​ people, "How often do you eat out for​ dinner, instead of at​ home?" The frequencies were as follows. Response Frequency Never 307 Rarely 600 Sometimes 945 Most of the time 268 Always 65

Never: .141 Rarely: .275 Sometimes: .433 Most of the time: .123 Always: .030

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E={3, 5, 9}.

P(E)= .3 use this formula to solve: P(E)=N(E)/N(S)**N(E)-number of outcomes in E**N(S)- number of outcomes in S

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E=​"an odd number less than 8​."

PE= .04

Describe the difference between classical and empirical probability.

The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes.

Which of the following numbers could be the probability of an​ event? 1, -0.45, 1.5, 0.04, 0.22, 0

The numbers that could be a probability of an event are 0, 0.04, 0.22, 1

In a certain card​ game, the probability that a player is dealt a particular hand is 0.41. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 41 times? Why or why​ not?

The probability 0.41 means that approximately 41 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 41 times since the probability refers to what is expected in the​ long-term, not​ short-term.

Why is the following not a probability​ model? Color Probability Red 0.2 Green -0.3 Blue 0.1 Brown 0.3 Yellow 0.3 Orange 0.4 Determine why it is not a probability model. Choose the correct answer below.

This is not a probability model because at least one probability is less than 0.

What is the probability of an event that is​ impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible?

What is the probability of an event that is​ impossible? 0 Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible? NO

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​? 0.5

The Wall Street Journal regularly publishes an article entitled​ "The Count." In one​ article, The Count looked at 1000 randomly selected home runs in Major League Baseball. Complete parts​ (a) through​ (d) below. ​(a) Of the 1000 home​ runs, it was found that 90 were caught by fans. What is the probability that a randomly selected home run is caught by a​ fan? (b) Of the 1000 home​ runs, it was found that 257 were dropped when a fan had a legitimate play on the ball. What is the probability that a randomly selected home run is​ dropped? (c) Of the 90 caught​ balls, it was determined that 39 were barehanded​ catches, 44 were caught with a​ glove, and 7 were caught in a hat. What is the probability a randomly selected caught ball was caught in a​ hat? Interpret this probability. (d) Of the 257 dropped​ balls, it was determined that 206 were barehanded​ attempts, 41 were dropped with a​ glove, and 10 were dropped with a failed hat attempt. What is the probability a randomly selected dropped ball was a failed hat​ attempt? Interpret this probability.

​(a) .09 =90/1000 (b) .257 =257/1000 (c) The probability is approximately .078. So, for every 1000 home runs caught by fans, we expected about 78 to have been caught in a hat. 7/90=.078 .78x100=78 (d) The probability is approximately .039. So, for every 1000 home runs dropped when a fan had a play o the ball, we expected about 39 to have been a failed hat attempt.

A survey of 100 randomly selected high school students determined that 33 play organized sports. ​(a) What is the probability that a randomly selected high school student plays organized​ sports? ​(b) Interpret this probability. ​(b) Choose the correct answer below.

​(a) The probability that a randomly selected high school student plays organized sports is .33 33/100=.33 (b) If​ 1,000 high school students were​ sampled, it would be expected that about 330 of them play organized sports. .33x1000=330

A bag of 100 tulip bulbs purchased from a nursery contains 20 red tulip​ bulbs, 30 yellow tulip​ bulbs, and 50 purple tulip bulbs. ​(a) What is the probability that a randomly selected tulip bulb is​ red? ​(b) What is the probability that a randomly selected tulip bulb is​ purple? ​(c) Interpret these two probabilities

​(a) The probability that a randomly selected tulip is red is .2 =20/100 ​(b) The probability that a randomly selected tulip bulb is purple is .5 =50/100 (c) If 100 tulip bulbs were sampled with replacement, one would expect about 20 of the bulbs to be red and about 50 of the bulbs to be purple.