Is a good hitter in baseball who has struck out the last six times due for a hit his next time up?
1Select all VALID probabilities values.
0%
1.01
110%
1
49/50
-0.25
50/49
Question 2Is a good hitter in baseball who has struck out the last six times due for a hit his next time up?
The Law of Large Numbers predicts the hitter is due for a hit.
This is an example of the Law of Averages. Yes, the hitter is now due for a hit.
The Law of Large Numbers predicts the hitter is not due for a hit.
This is an example of the so-called Law of Averages. No, the hitter is not due for a hit because the Law of Averages is non-existent and doesn’t predict anything.
Question 3After many observations, the relative frequency = # of events of interest / total # events appears to settle down to a constant value.
This is an example of the
Law of Averages.
Law of Large Numbers
Question 4How many permutations can be formed by sampling 3 things from 8 different things without replacement?
Question 5How many combinations of 3 people can be formed from 7 people?
Question 6Mutually Exclusive Events
If event A and event B cannot occur jointly (simultaneously), P(A and B) = 0, and A and B are called mutually exclusive events. So, if a local zoo only had mammals and reptiles, the sample space for types of zoo animals would be only mammals and reptiles.
Based on the zoo that had only mammals and reptiles, the sample space for this question contains only Mammals and Reptiles.
Choose the statements which are true for this scenario.
P(Mammal and Reptile) < 0
P(Mammal or Reptile) = 0, or impossible
P(Mammal or Reptile) = 1, or certain
P(Mammal and Reptile) > 0, or possible
P(Mammal and Reptile) = 0, or impossible
Question 7Toss 2 dice, and let the event be the sum of the values of the top faces. The possible outcomes are computed inside the following table at the intersection of the row of the “toss of 1st die” and the column of “toss of 2nd die”:
Because there are 36 outcomes, the probability of a sum = frequency of the sum/36.
So, the probabilities of the sums are
Sum Probability
2 1/36
3 2/36
4 3/36
5 4/36
6 5/36
7 6/36
8 5/36
9 4/36
10 3/36
11 2/36
12 1/36
Only one of the sums 2 through 12 can occur in a single toss of the dice. These are mutually exclusive events. The Simple Addition Rule P(A or B) = P(A) + P(B applies).
Additional Reading
Match the items on the left to the items on the right.
0.000
0.889
0.583
1.P(X at least 7)
2.P(X is not 9)
3.P(X = 1)
Question 8What is the probability of choosing a red card or a King from a deck of 52 cards?
For this event, choosing a red card or choosing a King, where choosing a red card and choosing a King may occur jointly, which rule applies?
Simple Addition Rule: P(A or B) = P(A) + P(B)
Simple Multiplication Rule: P(A and B) = P(A)*P(B)
General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
General Multiplication Rule: P(A and B) = P(A) X P(B | A)
Question 9P(A) = 0.500
P(B) = 0.200
P(A and B) = 0.100
Are events A and B independent?
True
False
Question 10When are events A and B dependent?
P(A and B) = 0
P(A and B) = P(A) x P(B)
P(A and B) > 0, and
P(A and B) ≠ P(A) x P(B)
Question 11Two customers enter a store. Independently, they make decisions to purchase or not to purchase. The following diagram shows how the outcomes can occur and combine with red bolding of sequence Customer 1 does not purchase and Customer 2 does not purchase.
The possible outcomes are shown on the right. If the event is the number of purchases, 3 events are possible: 0 purchases, 1 purchase, and 2 purchases.
Which one rule applies to the sequence of independent outcomes of Customer 1 and Customer 2?
General Multiplication Rule: P(A and B) = P(A) X P(B | A)
General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
Simple Addition Rule: P(A or B) = P(A) + P(B)
Simple Multiplication Rule: P(A and B) = P(A)*P(B)
Question 12Assume the following new probabilities:
P(Customer makes a purchase) = 0.900
P(Customer does not make a purchase) = 1- 0.900
Compute the probability that neither customer purchases (# purchases = 0), and enter your answer with 3 decimal places.
Question 13 Assume the following newest probabilities:
P(Customer makes a purchase) = 0.650
P(Customer does not make a purchase) = 1- 0.650
Compute the P(1 purchase), and enter your answer with 3 decimal places.
Question 14 There are two mutually exclusive reasons for visiting the emergency room of the local hospital: it is either an emergency or it is not an emergency. If the probability that a patient visiting the emergency room has an emergency is 0.65, what is the probability that the next patient has an emergency and the patient after the next one does not have an emergency? Assume that the patients arrive at the emergency room independently. (Round to three decimal places.)
Question 15 P(Male) is a ______ probability.
Marginal
Conditional
Joint
Question 16Republican Democrat Independent
Female 0.144 0.072 0.194
Male 0.121 0.183 ?
Compute the probability of the event Democrat, and enter your answer with 3 decimal places.
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