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28.10.2020 •
Mathematics
A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)
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Ответ:
A. Sample space = 6
B. 0.17
C. No
D. Yes
Step-by-step explanation:
A. The sample space of an experiment is the set of all possible outcomes of that experiment.
since there are three colours and 2 outcomes for a coin toss,
sample space = 3 * 2 = 6
B. Probability of picking a green first = 4/12 = 1/3
probability of a tail = 1/2
Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17
C. No.
Considering the two events;
A; green card is picked first
C ; a green or red card is picked
There is an intersection point for the two events. Therefore, they are not mutually exclusive.
D. Yes.
Considering the two events;
A; green card is picked first
B ; a blue or red card is picked
There is no intersection point for the two events. Therefore, they are mutually exclusive.
Ответ:
The circle is centered at (-8,3) and has a diameter of 20.
Step-by-step explanation:
The radius is 10 because you would take the square root of 100. To find the diameter you would multiply the radius by 2.