Section 7A

Section 7A

Fundamentals of Probability

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15. A restaurant has a special menu that features two choices of salad, eight choices of entree, and six choices of dessert. How many different three-course meals could you order?

15. A restaurant has a special menu that features two choices of salad, eight choices of entree, and six choices of dessert. How many different three-course meals could you order?

•  $\frac{?}{salad}^{\cdot}\frac{?}{entree}^{\cdot}\frac{?}{dessert}$ 

•  $\frac{2}{salad}^{\cdot}\frac{8}{entree}^{\cdot}\frac{6}{dessert}$  

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Use the theoretical method to determine the probability of the following outcomes and events. State any assumptions that you make.

23. Randomly flipping a coin twice and getting heads up twice.

23. Randomly flipping a coin twice and getting heads up twice.

• HH, HT, TH, TT

•  $P\left(A\right)=\frac{number\ of\ times\ A\ occurs}{total\ number\ of\ observations}$  

•  $P\left(2\ heads\right)=\frac{number\ of\ times\ 2\ heads\ occurs}{total\ number\ of\ observations}=\frac{1}{4}$  

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29. The local weather forecast has been accurate for 15 of the past 27 days. Based on this fact, what is the relative frequency probability that the forecast for tomorrow will be accurate?

Make a probability distribution for the given set of events. You may use either a table or a graph (or both).

41. The sums that result when two fair 4-sided dice (tetrahedrons) are tossed.

• List all possible outcomes, then find the sums.

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Use the definition of odds in betting to find the following odds.

47. The odds on (against) your bet are 3 to 5. If you bet $20 and win, how much will you gain?

Hint: Odds on are read backwards, so for ever $5 you bet, you will receive $3 in prize money.

You will get back the $20 you played, plus you will receive

in prize money.

Multiple Choice

Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probabilities. If you use the subjective method, explain your reasoning.

65. Not hearing your favorite group on a random shuffle of your playlist that has 889 songs, of which 127 are by your favorite group

• Theoretical

• Relative Frequency

• Subjective

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Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probabilities. If you use the subjective method, explain your reasoning.

65. Not hearing your favorite group on a random shuffle of your playlist that has 889 songs, of which 127 are by your favorite group

65. Not hearing your favorite group on a random shuffle of your playlist that has 889 songs, of which 127 are by your favorite group

• 889 - 127 = 762

• 762/889 = 6/7

Open Ended

67. Suppose you reach in and draw two marbles at random from a bag containing 10 white marbles (W), 10 black marbles (B), and 10 red marbles (R).

a. List all possible outcomes of this process (for example, RR, BW, and so on).

b. Make a table or graph showing the probability distribution for the events of 0, 1, and 2 black marbles.

67. Suppose you reach in and draw two marbles at random from a bag containing 10 white marbles (W), 10 black marbles (B), and 10 red marbles (R).

a. List all possible outcomes of this process (for example, RR, BW, and so on).

• WW, WB, WR,

• BW, BB, BR,

• RW, RB, RR

Open Ended

67. Suppose you reach in and draw two marbles at random from a bag containing 10 white marbles (W), 10 black marbles (B), and 10 red marbles (R).

b. Make a table or graph showing the probability distribution for the events of 0, 1, and 2 black marbles.

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73. Gender Politics. The following table gives the gender and political party of the 100 delegates at a political convention. Suppose you encounter a delegate at random.

a. What is the probability that you meet a man?

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73. Gender Politics. The following table gives the gender and political party of the 100 delegates at a political convention. Suppose you encounter a delegate at random.

b. What is the probability that you meet a Democrat?

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73. Gender Politics. The following table gives the gender and political party of the 100 delegates at a political convention. Suppose you encounter a delegate at random.

c. What is the probability that you do not meet an I­ndependent?

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73. Gender Politics. The following table gives the gender and political party of the 100 delegates at a political convention. Suppose you encounter a delegate at random.

d. What is the probability that you meet a male Republican?

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73. Gender Politics. The following table gives the gender and political party of the 100 delegates at a political convention. Suppose you encounter a delegate at random.

e. What is the probability that you meet someone who is not a female Republican? What is the probability that you meet someone who is not a female Republican?