5.2 Probability Rules

A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses?

• 996

• 998

• 1000

• 1002

• 1996

Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on his data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model?

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• 
• 
• 
• 

The two-way table gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender.

You select one musician from this group at random. What is the probability that this person plays a woodwind?

• 0.091

• 0.136

• 0.159

• 0.182

• 0.571

The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender.

You select one musician from this group at random. If the person is a male, what is the probability that he plays a woodwind?

• 0.091

• 0.136

• 0.159

• 0.182

• 0.571

The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender.

You select one musician from this group at random. Which of the following statement is true about the events “Plays a woodwind” and “Male?”

• The events are mutually exclusive and independent.

• The events are not mutually exclusive but they are independent.

• The events are mutually exclusive, but they are not independent.

• The events are not mutually exclusive, nor are they independent.

• The events are independent, but we do not have enough information to determine if they are mutually exclusive.

A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or a 6?

• 2/3

• 1/2

• 3/8

• 1/3

• 1/4

Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then

• P(A or B) = 1.0.

• P(A and B) = 0.16.

• P(A and B) = 1.0.

• P(A or B) = 0.16.

• both (a) and (b) are true.

A randomly selected student is asked to respond Yes, No, or Maybe to the question “Do you intend to vote in the next presidential election?” The sample space is { Yes, No, Maybe }. Which of the following represents a legitimate assignment of probabilities for this sample space?

• 0.4, 0.4, 0.2

• 0.4, 0.6, 0.4

• 0.3, 0.3, 0.3

• 0.5, 0.3, –0.2

• ¼, ¼, ¼

Select a random integer from –100 to 100. Which of the following pairs of events are mutually exclusive (disjoint)?

• A: the number is odd; B: the number is 5

• A: the number is even; B: the number is greater than 10

• A: the number is less than 5; B: the number is negative.

• A: the number is above 50; B: the number is less than 20.

• A: the number is positive; B: the number is odd.

The probability of any outcome of a random phenomenon is

• the precise degree of randomness present in the phenomenon.

• any number as long as it is greater than 0 and less than 1.

• either 0 or 1, depending on whether or not the phenomenon can actually occur or not.

• the proportion of times the outcome occurs in a very long series of repetitions.

• none of the above.