DM Flashcard Probability Basics, Addition & Multiplication Rules

Front

What is the probability of selecting a blue star from a box containing 25 gold stars, 75 red stars, and 50 blue stars?

Back

The probability of selecting a blue star is calculated as follows: \( P(Blue) = \frac{Number\ of\ Blue\ Stars}{Total\ Number\ of\ Stars} = \frac{50}{150} = \frac{1}{3} \)

Front

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

Back

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

Front

What is the probability of not landing on A if a spinner has 2 sections labeled A and 6 sections labeled B?

Back

The probability of not landing on A is: \( P(not\ A) = \frac{Number\ of\ Non-A\ Sections}{Total\ Sections} = \frac{6}{8} = \frac{3}{4} \)

Front

What is the difference between independent and dependent events?

Back

Independent events do not affect each other's outcomes, while dependent events do. For example, drawing cards without replacement is a dependent event.

Front

If a bag contains 30 pieces of candy (15 grape, 7 cherry, 3 lemon, 5 strawberry), what is the probability of selecting a lemon?

Back

The probability of selecting a lemon is: \( P(Lemon) = \frac{Number\ of\ Lemons}{Total\ Candies} = \frac{3}{30} = \frac{1}{10} \)

Front

What is the probability of drawing two aces in succession without replacement? Are these events independent or dependent?

Back

These events are dependent because the outcome of the first draw affects the second draw.

Front

What is the probability of landing on red first and then blue on a spinner spun twice? Are these events independent or dependent?

Back

These events are independent because the outcome of the first spin does not affect the outcome of the second spin.

Front

How do you calculate the probability of compound events?

Back

For dependent events: \( P(A \text{ and } B) = P(A) \times P(B|A) \) and for independent events: \( P(A \text{ and } B) = P(A) \times P(B) \)

Front

What is the total number of outcomes when rolling a six-sided die?

Back

The total number of outcomes when rolling a six-sided die is 6.

Front

If a spinner has 8 equal sections, what is the probability of landing on any specific section?

Back

The probability of landing on a specific section is: \( P(Specific\ Section) = \frac{1}{Total\ Sections} = \frac{1}{8} \)