Probability Tree Diagrams & Relative Frequency

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.

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.

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.

Front

How do you calculate relative frequency?

Back

Relative frequency = \( \frac{\text{Number of successful outcomes}}{\text{Total number of trials}} \)

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.

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 \( \left(\frac{1}{8}\right) \times \left(\frac{1}{8}\right) = \frac{1}{64} \).

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 \( \frac{3}{10} \times \frac{2}{9} = \frac{6}{90} \).

Front

How do you find the total number of outfit combinations?

Back

Multiply the number of choices for each clothing item. For example, 3 tops, 2 pants, and 2 shoes result in 3 * 2 * 2 = 12 outfits.

Front

What is the formula for calculating the probability of independent events?

Back

For independent events A and B, the probability of both occurring is \( P(A \text{ and } B) = P(A) \times P(B) \).

Front

What is the difference between independent and dependent events in probability?

Back

Independent events do not affect each other's outcomes, while dependent events do; the outcome of one event influences the outcome of another.