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
