Question

applying the multiplication rule
a bag contains the following fourteen marbles.
deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. what is the probability he will choose one green marble and then one red marble? express the probabilities in fraction form.
p(green) =
p(red) =
p(green and red) =

Explanation:

Step1: Calculate P(green)

Count the green marbles. There are 5 green marbles out of 14 total marbles. So $P(\text{green})=\frac{5}{14}$.

Step2: Calculate P(red)

Count the red marbles. There are 2 red marbles out of 14 total marbles. So $P(\text{red})=\frac{2}{14}=\frac{1}{7}$.

Step3: Calculate P(green and red)

Since the events are independent (because the marble is replaced), use the multiplication - rule for independent events $P(A\text{ and }B)=P(A)\times P(B)$. So $P(\text{green and red})=\frac{5}{14}\times\frac{1}{7}=\frac{5}{98}$.

Answer:

$P(\text{green})=\frac{5}{14}$
$P(\text{red})=\frac{1}{7}$
$P(\text{green and red})=\frac{5}{98}$