Answer to Question #139024 in Statistics and Probability for Mr A

Question

Suppose a graphing calculator is used to choose a random integer (whole #) between 1 and 60, with each integer having an equal chance of being selected. (2 pts each)

a) What is the probability that the number chosen is greater than 39?

b) Use the Addition Rule to find the probability that the calculator selects a number that is greater than 39 or is an even number less than 15.

c) Use the Addition Rule to find the probability that the calculator selects a number that is either greater than 39 or is an even number.

2. An instructor collects the home addresses of each student in a class of 30 students. Suppose A represents the event that all the students in the class live on different streets. (2 pts each)

a) Describe, in a sentence, what the event (A complement) represents.

Answer 1

a) Let A be the event that the number chosen is greater than 39

$$40,41,42,43,44,45,46,47,48,49,50,$$

$$51,52,53,54,55,56,57 ,58,59,60$$

There are 21 such numbers. Than the probability that the number chosen is greater than 39 is

$$P(A)=\dfrac{21}{60}=\dfrac{7}{20}=0.35$$

b) Let A be the event that the calculator selects a number that is greater than 39.

Let B be the event that the calculator selects a number that is an even number less than 15

$$2,4,6,8,10,12$$

$$P(A)=\dfrac{7}{20}=0.35$$

$$P(B)=\dfrac{6}{60}=\dfrac{1}{10}=0.1$$

The probability that the calculator selects a number that is greater than 39 or is an even number less than 15 is

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)=$$

$$=0.35+0.1-0=0.45$$

c) Let A be the event that the calculator selects a number that is greater than 39.

Let C be the event that the calculator selects a number that is an even number.

$$P(A)=\dfrac{7}{20}=0.35$$

There are 30 even numbers between 1 and 60

$$P(C)=\dfrac{30}{60}=\dfrac{1}{2}=0.5$$

There are 11 even numbers greater than 39 and not geater than60

$$40,42,44,46,48,50,52,54,56,58,60$$

The probability that the calculator selects a number that is either greater than 39 or is an even number is

$$P(A\cup C)=P(A)+P(C)-P(A\cap C)=$$

$$=0.5+0.35-\dfrac{11}{60}=\dfrac{2}{3}$$

2. Suppose $A$ represents the event that all the students in the class live on different streets. Then the event $A^C$represents the event that not all the students in the class live on different streets: at least two students in the class live on the same street.