Question

determine whether the following individual events are independent or dependent. then find the probability of the combined event.

rolling two 5s followed by one 3 on three tosses of a fair die.

choose the correct answer below.
(type an integer or a simplified fraction.)

a. the individual events are dependent. the probability of the combined event is
b. the individual events are independent. the probability of the combined event is

Explanation:

Determine independence of the events

Using the Probability knowledge point
The outcome of any single die toss does not affect the outcome of subsequent tosses. Therefore, the individual events of rolling a 5 on the first toss, a 5 on the second toss, and a 3 on the third toss are independent.

Calculate the probability of each individual event

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the combined probability

Using the Probability knowledge point

$$
LATEXBLOCK1
$$

Answer:

• A. The individual events are dependent. The probability of the combined event is \(\frac{1}{216}\)
• B. The individual events are independent. The probability of the combined event is \(\frac{1}{216}\) (Correct answer)