Question

you draw a marble from a bag that has 4 red, 2 blue, and 3 green marbles in it. you also flip a coin. what is the probability you will draw a blue marble and flip heads? a. \\( \frac { 1 } { 9 } \\) b. \\( \frac { 13 } { 18 } \\) c. 1 d. 2

Explanation:

Step1: Calculate the probability of drawing a blue marble

The total number of marbles is \(4 + 2+3=9\). The probability of drawing a blue marble \(P(\text{blue})\) is \(\frac{\text{number of blue marbles}}{\text{total number of marbles}}=\frac{2}{9}\).

Step2: Calculate the probability of flipping heads

The probability of flipping heads \(P(\text{heads})\) for a fair coin is \(\frac{1}{2}\).

Step3: Use the multiplication rule for independent events

Since drawing a marble and flipping a coin are independent events, the probability of both events occurring is \(P = P(\text{blue})\times P(\text{heads})\). Substitute the values: \(P=\frac{2}{9}\times\frac{1}{2}\).

$$
LATEXBLOCK0
$$

Answer:

A. \(\frac{1}{9}\)