Question

marbles problems
fill in the blank 3 points
find the probability of drawing a glass marble. p(glass) =
find the probability that a random marble from the above jar is glass, given that its green. p(glass | green) =
are events \glass\ and \green\ independent events?
fill in the blank 1 point
find the probability of drawing a red marble. p(red)=
find the probability of drawing a red marble, given that its steel. p(red | steel) =
based on your answers, are events
ed\ and \steel\ independent events? (you may need to reduce the fractions to be sure.)

Explanation:

Step1: Recall probability formula

The probability of an event $A$ is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Find $P(\text{red})$

The total number of marbles is 81, and the number of red marbles is 39. So $P(\text{red})=\frac{39}{81}=\frac{13}{27}$.

Step3: Recall conditional - probability formula

The conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$, or $P(A|B)=\frac{\text{Number of outcomes in }A\cap B}{\text{Number of outcomes in }B}$.

Step4: Find $P(\text{red}|\text{steel})$

The number of steel marbles is 27, and the number of red - steel marbles is 13. So $P(\text{red}|\text{steel})=\frac{13}{27}$.

Answer:

$P(\text{red})=\frac{13}{27}$
$P(\text{red}|\text{steel})=\frac{13}{27}$