Multiplication Rule for Probability

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•
Mathematics
•
8th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Multiplication Rule for Probability?
Back
The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. For dependent events, the probability of the second event is affected by the first.
2.
FLASHCARD QUESTION
Front
If the probability of event A is P(A) and the probability of event B is P(B), what is the probability of both A and B occurring?
Back
For independent events: P(A and B) = P(A) * P(B). For dependent events: P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given A has occurred.
3.
FLASHCARD QUESTION
Front
How do you calculate the probability of drawing two marbles from a bag without replacement?
Back
Calculate the probability of drawing the first marble, then multiply it by the probability of drawing the second marble given the first has been drawn. For example, if there are 5 red and 3 blue marbles, the probability of drawing a red first and then a blue is: P(Red) * P(Blue|Red) = (5/8) * (3/7).
4.
FLASHCARD QUESTION
Front
What is the probability of selecting a white marble from a bag containing 12 red, 6 white, and 2 blue marbles?
Back
The probability of selecting a white marble is the number of white marbles divided by the total number of marbles: P(White) = 6/(12+6+2) = 6/20 = 3/10.
5.
FLASHCARD QUESTION
Front
In a key ring with 12 keys, 3 of which open a door, what is the probability that a randomly selected key does not open the door?
Back
The probability that a randomly selected key does not open the door is the number of keys that do not open the door divided by the total number of keys: P(Not Open) = (12-3)/12 = 9/12 = 3/4.
6.
FLASHCARD QUESTION
Front
What is the probability of selecting a news magazine first and then a sports magazine from a stack of 5 news and 10 sports magazines?
Back
The probability of selecting a news magazine first is 5/15. After selecting a news magazine, there are 14 magazines left, so the probability of selecting a sports magazine next is 10/14. Therefore, P(News then Sports) = (5/15) * (10/14) = 1/3 * 5/7 = 5/21.
7.
FLASHCARD QUESTION
Front
If a bag contains 20 boxes of cereal A and 10 boxes of cereal B, what is the probability that neither box selected has a prize?
Back
The probability that the first box does not have a prize is 29/30 (29 non-prize boxes out of 30 total). The probability that the second box also does not have a prize is 28/29. Therefore, P(Neither has a prize) = (29/30) * (28/29) = 28/30 = 14/15.
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