Mutually Exclusive and Independent Events

A wheel contains eight slices, numbered sequentially 1 through 8. The probability of landing on each slice is equal. If the wheel is spun three times, what is the probability that the first spin is 4 or less, the second spin is 6 or less, and the third spin is 8 or less?

3/8 or .375

A card is drawn randomly from a standard 52-card deck, examined, and then shuffled back into the original deck. A second card is drawn randomly from the deck. What is the probability that the first card was a red card and the second card is a black card? A. 1/4 B. 1/2 C. 1 D. these events are not independent

A

Which of the following actions is an example of independent events? A. choosing an almond out of a bag of mixed nuts, and then choosing a walnut out of a different bag of nuts B. choosing an almond out of a bag of mixed nuts, and then choosing a walnut out of the same bag of mixed nuts C. choosing an almond out of a bag of mixed nuts, and then choosing another almond out of the same bag of mixed nuts D. choosing an almond out of a bag of mixed nuts, removing the rest of the almonds in the bag, and then choosing another type of nut

A

The next four batters on a baseball team have hitting percentages of 0.400, 0.325, 0.250, and 0.300, respectively. The team currently has two outs. If any player gets an out, the next player or players will not get an opportunity to bat. What is the probability that the fourth player will have an opportunity to bat? A. 0 B. 13/400 C. 17/40 D. 33/40

B

Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth. A. 0.056 B. 0.139 C. 0.167 D. 0.278

B

Which of the following describes an example of independent events? A. generating a random number between 1 and 25, and then generating another random number between 1 and 25, excluding the first one picked B. generating a random number between 1 and 25, and then generating another random number between 1 and 25, including the first one picked C. generating a random number between 2 and 25, and then generating another random number less than the first one picked D. generating a random number between 1 and 24, and then generating another random number greater than the first one picked

B

Which of the following statements best defines independent events? A. Two events are independent events if it is impossible for the two events to occur simultaneously. B. Two events are independent events if the occurrence of one event has no effect on the probability of the other. C. Two events are independent events if the intersection between the sample spaces of the two events is not empty. D. Two events are independent events if the union of the sample spaces of the two events is not empty.

B

Which of the following describes an example of mutually exclusive outcomes A and B for throwing a single 6-sided die? A. A = the outcome is odd, B = the outcome is 3 B. A = the outcome is in (1,2,3,4), B= the outcome is in (4,5,6) C. A = the outcome is odd, B = the outcome is even D. A = the outcome is less than 6, B = the outcome is more than 1

C

Which of the following does not describe an example of mutually exclusive outcomes 2004-06-03-04-00_files/i0080000.jpg and 2004-06-03-04-00_files/i0080001.jpg for drawing a card at random from a standard 52-card deck? A. A = the card is red, B = the card is black B. A = the card is less than 8, B = the card is an 8 C. A = the card is black, B = the card is a heart or a spade D. A = the card is red, B = the card is a spade

C

A card is drawn randomly from a standard 52-card deck, examined, and then discarded. A second card is drawn randomly from the remaining deck. What is the probability that the first card was a black card and the second card was a red card? A. 1/4 B. 1/2 C. 1 D. these events are not independent

D

A sock drawer contains winter socks and summer socks. Both varieties come in two colors: red and blue. There are two pairs each of red summer socks and red winter socks, and one pair each of blue summer socks and blue winter socks. If a sock is selected randomly, what is the probability it will be a red sock or a winter sock? A. 1/9 B. 1/3 C. 2/3 D. 5/6

D

Which of the following describes an example of mutually exclusive outcomes A and B for selecting a card at random from a standard 52-card deck? A. A = the card is an ace, B = the suit is a spade B. A = the card is a king, B = the suit is a heart C. A = the card is black, B = the suit is a club D. A = the card is 8 or less, B = the card is a king

D

Using this formula, calculate the probability of drawing a red card or any jack on a single random draw from a standard 52-card deck. A. 1/26 B. 1/2 C. 7/13 D. 15/26

not 1/26

Using this formula, calculate the probability of drawing a black card or any ten on a single random draw from a standard 52-card deck. A. 5/13 B. 13/26 C. 7/13 D. 15/26

not 15/26

Two standard number cubes are thrown simultaneously. What is the probability that the combined result of the two cubes is exactly 7, or that it is less than (but not equal to) 6? Round answer to the nearest thousandth. A. 0.444 B. 0.556 C. 0.667 D. 0.853

not C