Question

In: Statistics and Probability

1. (1 point) The range of probability is ​a. ​any value larger than zero ​b. ​any...

1. (1 point)
The range of probability is
​a. ​any value larger than zero
​b. ​any value between minus infinity to plus infinity
​c. ​zero to one
​d. ​any value between -1 to 1
2. (1 point)
Any process that generates well-defined outcomes is
​a. ​an event
​b. ​an experiment
​c. ​a sample point
​d. ​None of the other answers is correct.
3. (1 point)
The sample space refers to
​a. ​any particular experimental outcome
​b. ​the sample size minus one
​c. ​the set of all possible experimental outcomes
​d. ​both any particular experimental outcome and the set of all possible experimental outcomes are correct
4. (1 point)
An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is
​a. ​9
​b. ​14
​c. ​24
​d. ​36
5. (1 point)
When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the
​a. ​relative frequency method
​b. ​subjective method
​c. ​probability method
​d. ​classical method
6. (1 point)
Given that event E has a probability of 0.25, the probability of the complement of event E
​a. ​cannot be determined with the above information
​b. ​can have any value between zero and one
​c. ​must be 0.75
​d. ​is 0.25

If P(A) = 0.38, P(B) = 0.83, and P(A ∩ B) = 0.57; then P(A ∪ B) =
​a. ​1.21
​b. ​0.64
​c. ​0.78
​d. ​1.78
14. (1 point)
If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88; then P(A ∩ B) =
​a. ​0.2914
​b. ​1.9700
​c. ​0.6700
​d. ​0.2100
15. (1 point)
Two events are mutually exclusive if
​a. ​the probability of their intersection is 1
​b. ​they have no sample points in common
​c. ​the probability of their intersection is 0.5
​d. ​the probability of their intersection is 1 and they have no sample points in common
16. (1 point)
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =
​a. ​0.00
​b. ​0.15
​c. ​0.8
​d. ​0.2
17. (1 point)
If P(A|B) = P(A) then
​a. ​A and B are mutually exclusive
​b. ​A and B are dependent
​c. ​A and B are both mutually exclusive and dependent
​d. ​A and B are independent.
18. (1 point)
On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and a "cold" day is .15. Are snow and "cold" weather independent events (Hint: think about a joint probability table)?
​a. ​only if given that it snowed
​b. ​no
​c. ​yes
​d. ​only when they are also mutually exclusive
19. (1 point)
If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =
​a. ​0.76
​b. ​1.00
​c. ​0.24
​d. ​0.2
20. (1 point)
If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =
​a. ​0.62
​b. ​0.12
​c. ​0.60
​d. ​0.68

Solutions

Expert Solution

1) The range of probability is

c) zero to one.

2) Any process that generates well-defined outcomes is

b) ​an experiment

3) The sample space refers to

​c) ​the set of all possible experimental outcomes

4) An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

4*3*2 = 24

c) 24

5) When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the

​d. ​classical method

6) Given that event E has a probability of 0.25, the probability of the complement of event E

P(Ec ) = 1- P(E) = 1-0.25 = 0.75

c) must be 0.75

7)If P(A) = 0.38, P(B) = 0.83, and P(A ∩ B) = 0.57; then P(A ∪ B) =

  P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= 0.38+0.83-0.57 = 0.64

b) 0.64  

14) If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88; then P(A ∩ B) =

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

= 0.62+0.47-0.88 = 0.21

d) 0.2100

15)Two events are mutually exclusive if

  ​b) ​they have no sample points in common

16) If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =

P(A ∪ B) = P(A) + P(B) = 0.3+0.5 = 0.8

c) 0.8

17) If P(A|B) = P(A) then

  ​d)​A and B are independent.

18) On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and a "cold" day is .15. Are snow and "cold" weather independent events

P(snow and cold) = 0.15 =  P(snow) * P(cold) = 0.3*0.5 = 0.15

  c) ​yes

19) If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =

   P(A ∩ B) = P(A) * P(B) = 0.4*0.6 = 0.24

c) 0.24

20) If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - P(A)*P(B)

= 0.2+0.6 - 0.2*0.6 = 0.68

d) 0.68

****If you have any queries or doubts please comment below, if you're satisfied please give a like. Thank you!

orchestra answered 2 years ago
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