Question

The probability that you roll a 3 on a six-sided die is . The probability that you flip a coin that lands on tails is . The probability that you roll a 3 on a six-sided die and you flip a coin that lands on tails is . What is the probability of flipping a coin and it landing on tails, given that you rolled a 3 on a six-sided die? Are these two events independent? P(T|3) = ; therefore, events are independent because P(T|3) = P(T). P(T|3) = ; therefore, events are dependent because P(T|3) ≠ P(T). P(T|3) = ; therefore, events are dependent because P(T|3) ≠ P(T). P(T|3) = ; therefore, events are independent because P(T|3) = P(T).

Answer 1

P(T|3) = 1/2 ; therefore, events are independent because P(T|3) = P(T).

Explanation:

Answer 2

1/6; 1/2; 1/12; P(T|3) = 1/2; therefore, events are independent because P(T|3) = P(T).

Explanation:

The probability of rolling a 3 on a six-sided die is 1/6. This is because there is one 3 out of 6 possibilities.

The probability of flipping a coin on tails is 1/2. This is because there is one side "tails" out of 2 possibilities.

The probability of rolling a 3 and flipping tails is 1/6(1/2) = 1/12.

P(T|3) = P(3 and Tails)/P(3) = 1/12 / (1/6) = 1/12(6/1) = 6/12 = 1/2

Since P(T|3) = P(3), these are independent events.