1. Select which type of probability corresponds to each description. Select from
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Question
1. Select which type of probability corresponds to each description. Select from Theoretical (Classical), Relative Frequency, or Subjective.
a) Probabilities correspond to the long run frequency of an event occurring based on repeated experiments.
b) Explicitly count all of the possible outcomes and those of interest. Assume a mathematical model and derive probabilities from that model.
c) Use intuition or experience to assign probabilities.
2. What is the chance of drawing a king from a full deck of 52 cards? Enter your final answer as a fraction.
3.Consider flipping two fair coins. Determine the sample space below. Write your answer using set notation.
4. Consider the height (in inches) of a randomly selected STA student’s mother. Determine the sample space.
Write your answer using mathematical notation.
Hint: **Biologically plausible range for adult height is 48 to 84 inches.
5. Suppose an individual is drawing cards from a full deck of 52 cards. Are the events getting a spade and getting a jack mutually exclusive? Why or why not? In order to receive full credit, you must justify your answer using probability.
6. Determine whether or not the following numbers could be examples of a probability. Select from: Yes or No. (4 points, 1/2 point each)
a) 0.5
b) 0
c) 1.6
d) 1/7
e) -3
f) 1
g) 8
h) -0.456789
Explanation / Answer
Solution:-
1.
a) Theoretical (Classical):- Probabilities correspond to the long run frequency of an event occurring based on repeated experiments.
Subjective: - b) Explicitly count all of the possible outcomes and those of interest. Assume a mathematical model and derive probabilities from that model.
Relative Frequency: - c) Use intuition or experience to assign probabilities.
2) The chance of drawing a king from a full deck of 52 cards is 0.07692.
Number of king in a deck = 4
Total number of cards = 52
The chance of drawing a king from a full deck of 52 cards = 4/52 = 0.07692
3) Flipping two fair coins the sample space is
(H, H) (H, T), (T, H) (T, T)
S = {HH,HT,TH,TT}.
5) Events getting a spade and getting a jack are not mutually exclusive.
In probability, two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
Probability of getting spade = 13/52 = (1, 2,3, 4, 5, 6,7, 8, 9, 10, J, Q, K, A)
Probability of getting Jack = 4/52 = (JSpade, JClub, JDiamond, JHeart)
Hence these both event have Jack of spade in common so these events cannit be mutually exclusive.
6) Examples of a probability are :-
a) 0.5
b) 0
d) 1/7
f) 1
Probability is always positive lies between 0 and 1 including 0 and 1.
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