Introduction to Probability, statistics assignment help

  

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Due Sept 30
Name ____________
ASSIGNMENT 5A
1. For these problems, we’ll calculate probabilities by generating event space and sample spaces, counting, and then calculating. The
first example is worked for you.
a.
When flipping two coins, find the probability of getting one head and one tail. Note: count HT separate from TH
Sample Space: HH, HT, TH, TT
( ) = 4
Event Space: HT, TH
( ) = 2
( ) =
b.
( )
( )
= 2/4 = ½ or 0.5
When rolling one die, find the probability of getting a number greater than four.
Sample Space: ______________________________________________________ ( ) = _______
Event Space: _______________________________________________________ ( ) = _______
( ) =
c.
( )
( )
= ______________
When rolling a red die and a blue die, the probability of getting a sum less than 5.
Sample Space: _____________________________________________________________________
__________________________________________________________________ ( ) = _______
Event Space: _______________________________________________________ ( ) = _______
( ) =
d.
( )
( )
=______________
When flipping a coin four times, getting the sequence HTHT.
Sample Space: _____________________________________________________________________
__________________________________________________________________ ( ) = _______
Event Space: _______________________________________________________ ( ) = _______
( ) =
( )
( )
=______________
Due Sept 30
2.
Suppose you are planning to choose one card from a deck of 52 well-shuffled playing cards. Calculate the probabilities of each of
the following events. Reduce any fractions to lowest terms for your final answer.
a. What is the probability of choosing a red card?
_________
b. What is the probability of choosing a black queen? __________
c. What is the probability of choosing a jack? __________
d. What is the probability of choosing a diamond? __________
a. What is the probability that the chosen card is red and is not a face card? __________
3.
Label these probabilities as empirical or classical. (Yes, some are also subjective, but that’s not what I’m asking.)
a. I note that last summer it rained 6 days out of 90, so I assign P(rain tomorrow) = 6/90 = 0.067. _________________
b. A weather forecaster says his model predicts a 10% chance of rain tomorrow. ________________
c. I consider two horses at the track. One looks healthier, stronger, and more energetic, so I place the probability of that one
winning at about 0.3 (and hurry to the window to place a bet, since they are claiming he has a 0.1 chance and will give me
great odds). ___________________
d. I read that horse A has placed in 14 races in his career, and I assign him a probability of winning at 0.3. ______________
4.
Find the probability of rolling a blue die and a red die and the sum coming up 7. Use the principles you just used in the previous
problems. (Make sure and define an event as the number on each die; for example, 3-4 yields 7, and so does
4-3, but these are separate events. This will ensure all events have equal probability. )
Due Sept 30
5.
I am told the probability of it raining tomorrow is 0.3. I’m told the probability of it hailing tomorrow is 0.1. I then state that the
probability of it hailing or raining is 0.4.
a. What is wrong with this reasoning/conclusion?
b. I discover that the actual probability of rain or hail is 0.35. What Important statement can I infer regarding rain and hail
tomorrow?
6. Find the probability of:
a. picking a card that is red from a standard deck _____
b. picking a care that is a queen __________
c. picking a card that is a red queen ___________
d. picking a card that is either red or a queen __________
Note that you could have solved part d either by calculating P(redqueen) = P(red)+P(queen)-P(red queen) or by counting each of
the cards in the deck that are either red or queen. But since you had just solved a, b, and c, the first method makes more sense.
7.
Use the coin flipper in Canvas (just under the lecture slides) to perform an experiment. Change just the number of trials
(highlighted in yellow) and report your results in the table below:
number of trials
10
100
1000
10000
percent (to 3 decimals)
HH
HT
TH
TT
Do your results suggest that more trials will bring the results closer to the theoretical percentages? _____________________
…
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