Algebra: Probability of Independent Events assignment

Which statement correctly describes dependent events?

Two events are dependent if the outcome of the first event affects the outcome of the second event.

Two events, A and B, are independent. If P(A) = 0.3 and P(B) = 0.2, what is P(A and B)?

0.06

Consider a situation in which P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12. What is P(B and C)?

1/6

Three coins are flipped. What is P(heads, heads, heads)?

1/8

Andrea rolls a number cube twice. She determines P(even, then odd) = 1/2. Which statements are accurate? Check all that apply.

Andrea's solution is incorrect. The probability of each simple event is 1/2. The probability of the compound event is less than the probability of either event occurring alone. P(even, then odd) = P(odd, then even)

For an in-class demonstration, a teacher flips a fair coin 5 times, and each of the 5 times it lands on heads. A student argues that it is more likely to land on tails on the next, or 6th, flip. Is the student correct? Explain your reasoning.

Sample Response: The student's logic is incorrect. A coin being flipped 6 times is 6 independent events because the outcome of one flip of the coin does not affect the outcome of another flip. The probability of the next flip landing on heads is still 1/2.

A spinner contains 3 equal sections: one red, one yellow, and one blue. The possible results of two spins are shown in the tree diagram below. What is P(red, then yellow)?

1/9

A bag contains a variety of different-colored marbles. If P(red) = 1/2 , P(green) = 1/4, and P(red and green) = 1/8, which statement is true?

The events are independent because P(red) • P(green) = P(red and green).

Which events are independent? Check all that apply.

rolling two number cubes at the same time choosing a card, and then flipping a coin drawing a marble from a bag, replacing it, then drawing another marble flipping the same coin three times