Probability Tree Diagrams & Relative Frequency

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•
Mathematics
•
11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a probability tree diagram?
Back
A probability tree diagram is a graphical representation that shows all possible outcomes of a probability experiment, illustrating the paths leading to each outcome.
2.
FLASHCARD QUESTION
Front
How do you calculate the total number of outcomes in a probability tree diagram?
Back
Multiply the number of outcomes at each stage of the experiment. For example, rolling a die (6 outcomes) and flipping a coin (2 outcomes) results in 6 * 2 = 12 total outcomes.
3.
FLASHCARD QUESTION
Front
What is relative frequency?
Back
Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations, often expressed as a fraction or percentage.
4.
FLASHCARD QUESTION
Front
How do you calculate relative frequency?
Back
Relative frequency = \( \frac{\text{Number of successful outcomes}}{\text{Total number of trials}} \)
5.
FLASHCARD QUESTION
Front
If a coin is flipped 30 times and lands on tails 20 times, what is the relative frequency of tails?
Back
Relative frequency of tails = \( \frac{20}{30} = \frac{2}{3} \) or approximately 0.67.
6.
FLASHCARD QUESTION
Front
What is the probability of drawing two red counters from a bag with replacement?
Back
If there is 1 red counter in a bag of 8, the probability of drawing two red counters with replacement is \( \left(\frac{1}{8}\right) \times \left(\frac{1}{8}\right) = \frac{1}{64} \).
7.
FLASHCARD QUESTION
Front
What is the probability of drawing two red counters from a bag without replacement?
Back
If there are 3 red counters in a bag of 10, the probability of drawing two red counters without replacement is \( \frac{3}{10} \times \frac{2}{9} = \frac{6}{90} \).
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