statistics test 3

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."

(1,3,5,7,9) 5/10=.5

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 even number less than 9​."

(2,4,6,8) 4/10=.4

1) Is the following a probability​ model? 2) What do we call the outcome ​"brown​"? red- 0.2 green- 0.2 blue- 0.1 brown- 0 yellow- 0.3 orange- 0.2

1) Yes​, because the probabilities sum to 1 and they are all greater than or equal to 0 and less than or equal to 1. 2) impossible event (bc equal to zero)

A golf ball is selected at random from a golf bag. If the golf bag contains 6 green ​balls, 9 brown ​balls, and 9 yellow ​balls, find the probability of the following event. The golf ball is green or brown.

6+9+9= 24 15/24=.625

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A​ balls, 7 type B​ balls, and 4 type C​ balls, find the probability that the golf ball is not a type A ball.

7+4=11 11/16=.6875

Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

independent

The word "AND" in probability implies that we use the​ ________ rule.

multiplication rule

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 twelve must be one eleventh . What is wrong with​ Bob's reasoning?

the experiment does not has equally likely outcomes

A survey of 900 randomly selected high school students determined that 84 play organized sports. ​(a) What is the probability that a randomly selected high school student plays organized​ sports? ​(b) Interpret this probability.

(a)84/900=.093 (b).093*1000=93

About 11​% of the population of a large country is nervous around strangers. If two people are randomly​ selected, what is the probability both are nervous around strangers​? What is the probability at least one is nervous around strangers​?

.11*.11=.0121 1-.11=.89 .89*.89= .7921 1-.7921= .2079

According to a certain​ country's department of​ education, 44.1​% 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?

.441

How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999​?

1-(probability)^#

Find the probability ​P(Upper E^c​) if ​P(E)=0.34.

1-.34=.66

What does it mean for an event to be​ unusual? Why should the cutoff for identifying unusual events not always be​ 0.05?

An event is unusual if it has a low probability of occurring. The choice of a cutoff should consider the context of the problem.

Determine if the following statement is true or false. When two events are​ disjoint, they are also independent.

False

According to a center for disease​ control, the probability that a randomly selected person has hearing problems is 0.145. The probability that a randomly selected person has vision problems is 0.082. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these​ probabilities? Why or why​ not?

No, because hearing and vision problems are not mutually exclusive.​ So, some people have both hearing and vision problems. These people would be included twice in the probability.

General Addition rule

P(E or D)=P(E)+P(D)-P(E and D)

In a certain card​ game, the probability that a player is dealt a particular hand is 0.34. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 34 ​times? Why or why​ not?

The probability 0.34 means that approximately 34 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 34 times since the probability refers to what is expected in the​ long-term, not​ short-term.

Suppose you toss a coin 100 times and get 65 heads and 35 tails. Based on these​ results, what is the probability that the next flip results in a head​?

The probability that the next flip results in a head is approximately . 65 (65/100) use formula( relative freq of E= Freq of E/ # of trials

The word "OR" in probability implies that we use the _________________ Rule.

addition

a______is any collection of outcomes from a probability experiment.

event

In​ probability, a(n)​ ________ is any process that can be repeated in which the results are uncertain.

experiment

In a probability​ model, the sum of the probabilities of all outcomes must equal 1. T/F

true

Probability is a measure of the likelihood of a random phenomenon or chance behavior. T/F

true

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecting a ten or four. ​(b) Compute the probability of randomly selecting a ten or four or ace. ​(c) Compute the probability of randomly selecting a ten or club.

=.154 =.231 =.308

A gene is composed of two alleles. An allele can be either dominant or recessive. Suppose that a husband and​ wife, who are both carriers of the​ sickle-cell anemia allele but do not have the​ disease, decide to have a child. Because both parents are carriers of the​ disease, each has one dominant​ normal-cell allele​ (S) and one recessive​ sickle-cell allele​ (s). Therefore, the genotype of each parent is Ss. Each parent contributes one allele to his or her offspring with each allele being equally likely. Complete parts ​a) through ​c) below.

(a)SS,ss (b)The probability is .25. This means that there is a 25% chance that a randomly selected offspring will have​ sickle-cell anemia. (c)The probability is .5 This means there is a 50​% chance that a randomly selected offspring will be a​ carrier, but will not have​ sickle-cell anemia.

In a certain game of​ chance, a wheel consists of 30 slots numbered​ 00, 0,​ 1, 2,..., 28. To play the​ game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts​ (a) through​ (c) below.

(a)The sample space is​ {00, 0,​ 1, 2,..., 28​}. (b) Determine the probability that the metal ball falls into the slot marked 5.--- 1/30=.0333 If the wheel is spun 1000​ times, it is expected that about 33 of those times result in the ball landing in slot 5.-----.0333*1000=33.3~~33 (c)14/30=.4667 If the wheel is spun 100​ times, it is expected that about 47 of those times result in the ball landing on an odd number.

What is the probability of obtaining six heads in a row when flipping a​ coin? Interpret this probability.

.5^6= answer

A test to determine whether a certain antibody is present is 99.1​% effective. This means that the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.1​% of the time. The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.009. Suppose the test is given to five randomly selected people who do not have the antibody. ​(a) What is the probability that the test comes back negative for all five ​people? ​(b) What is the probability that the test comes back positive for at least one of the five ​people?

0.009-1=.991 .991^5= .9558 .9558-1= .0442

If events E and F are disjoint and the events F and G are​ disjoint, must the events E and G necessarily be​ disjoint? Give an example to illustrate your opinion.

No, events E and G are not necessarily disjoint. For​ example, E=​{0,1,2}, F=​{3,4,5}, and G={2,6,7} show that E and F are disjoint​ events, F and G are disjoint​ events, and E and G are events that are not disjoint.

Find the probability of the indicated event if ​P(E)equals0.40 and ​P(F)equals0.35. Find​ P(E and​ F) if​ P(E or ​F)equals0.70

P(E and F)= .05

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

P(E or F)= .75

if E and F are disjoint events, then P(E or F) =

P(E) + P(F)

If E and F are not disjoint​ events, then​ P(E or ​F)=_______.

P(E)+P(F)-P(E and F)

E=(1,2,3,4,5) F=(2,4) what are the outcomes of E AND F list the outcomes of the two number sets, are tell if mutually exclusive?

(2,4) not mutually exclusive because the have same number in both sets

A bag of 100 tulip bulbs purchased from a nursery contains 40 red tulip​ bulbs, 30 yellow tulip​ bulbs, and 30 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)40/100= .4 (b)30/100= .3 (c)If 100 tulip bulbs were sampled with​ replacement, one would expect about 40 of the bulbs to be red and about 30 of the bulbs to be purple.

A baseball player hit 61 home runs in a season. Of the 61 home​ runs, 21 went to right​ field, 18 went to right center​ field, 8 went to center​ field, 12 went to left center​ field, and 2 went to left field. ​(a) What is the probability that a randomly selected home run was hit to right​ field? ​(b) What is the probability that a randomly selected home run was hit to left​ field? ​(c) Was it unusual for this player to hit a home run to left​ field? Explain.

a) The probability that a randomly selected home run was hit to right field is .344 ​(b) The probability that a randomly selected home run was hit to left field is .033 (c)Yes, because​ P(left ​field)<0.05.

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

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 2/10=.2

Suppose that events E and F are​ independent, P(E)=.06, and P(F)= .06. what is the P(E and F)

0.6*0.6=.36

If a person flips a coin and then spins a six dash space spinner​, describe the sample space of possible outcomes using Upper H comma Upper T for the coin outcomes and 1 comma 2 comma 3 comma 4 comma 5 comma 6 for the spinner outcomes.

The sample space is S= H 1 ,H 2 ,H 3, H 4 , H 5 , H 6 , T 1 ,r T 2 , T 3, T 4 ,T 5 ,T 6​}.

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

True

(d) Determine the probability that a randomly selected multiple birth for women​ 15-54 years old involved a mother who was at least 40 years old. Interpret this result. Is it​ unusual? Find the probability that a randomly selected multiple birth for women​ 15-54 years old involved a mother who was at least 40 years old.

use disjoint