Question

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 probability of green

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

Step2: Calculate probability of red

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

Step3: Calculate probability of green and red

Since the draws are independent (due to replacement), we use the multiplication rule for independent events. $P(\text{green and red})=P(\text{green})\times P(\text{red})=\frac{5}{14}\times\frac{1}{7}=\frac{5}{98}$.

Answer:

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