Algebra: Probability of Independent Events assignment

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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


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