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Quiz 4: Probability

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
The following ordered pairs of numbers (x,y) were obtained in an experiment:
(1,2),(2,4),(3,6),(3,7).
Without performing calculations, what is the best description of the size of the correlation coefficient of the data ?
a) Slightly less than 1.   b) Positive.
c) Slightly greater than 2.   d) Slightly greater than 1.

 

Your answer is correct.
By inspection, we see that the correlation coefficient must be positive but the magnitude of the correlation coefficient can never be greater than 1.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 2

 
 
We are told that in a random experiment there are five possible outcomes. Which of the following statements is true ?
a) If, after 20 trials, one outcome has not been observed then the probability that it will occur in the next trial is increased.
b) If, after 20 trials, one outcome has been observed more often than the others then the probability that it will not occur in the next trial is increased.
c) If, after 20 trials, one outcome has not been observed then the probability that it will occur in the next trial is unchanged.
d) If the outcomes are equally likely then the trials are independent.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
In a random experiment the outcomes are independent so the first two statements are incorrect. We do not have enough information to comment on the probability of each outcome, so the fourth statement is incorrect.
Not correct. Choice (d) is false.
 

Question 3

 
 
A coin is tossed 6 times. What is the probability of exactly 2 heads occurring in the 6 tosses.
a) ( ) ( )6 6 1 2 2   b) ( ) 1 6 2
c) ( ) 1 6 3   d) (6 )( 1)6 2 3

 

Your answer is correct.
The two heads can occur in any of the six tosses, so there are ( ) 6 2 arrangements, with a probability of ( )6 1 2 for each arrangement.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 4

 
 
A coin is tossed 6 times. What is the probability of getting 2 heads, followed by 4 tails ?
a) ( ) ( ) 6 1 6 2 2   b) ( ) 1 6 2
c) ( 1)6 3   d) (6 )( 1)6 2 3

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 5

 
 
A coin is tossed and a fair six sided die is thrown. How many possible outcomes are there ?
a) 12   b) 6
c) 2   d) 8

 

Your answer is correct.
Each die face can come up with a head or a tail. The number of possible outcomes is therefore 6 + 6 = 12.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 6

 
 
Two fair dice are tossed. How many possible outcomes are there ?
a) 12   b) 6
c) 36   d) None of these.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
 

Question 7

 
 
Two fair dice are thrown. What is the probability of the sum of 10 being obtained for the two uppermost faces ?
a) -1 36   b) 1 4
c) 1 18   d) -1 12

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
The possible pairs of faces are (4,6), (5,5) and (6,4). That is, 3 out of a possible 36. The probability is therefore -3 36 = 1- 12.
 

Question 8

 
 
What is the value of (n ) r with n = 7 and r = 2 ?
a) 2520   b) 42
c) 21   d) 84

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
(n) r = n! --------- r!(n - r) ! = 7! ---- 2!5! = 7× 6 ----- 2 = 21.
Not correct. Choice (d) is false.
 

Question 9

 
 
A fair coin is tossed twice. What is the probability of obtaining a head and a tail ?
a) 1 2   b) 1 3
c) 1 4   d) 1 5

 

Your answer is correct.
The two possible outcomes are HT and TH, each of which has probability 1 4. The probability of a head and a tail is therefore 1 - 4 + 1 - 4 = 1 - 2.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 10

 
 
A coin is tossed until two heads occur on successive throws. The number of tosses is described by which of the following ?
a) It is a binomial distribution, B ( ) n, 12.
b) It is a binomial distribution, B ( 2) n,n.
c) It is not described by a binomial distribution.
d) It is described by a geometric distribution.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.