heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag…

heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag, replaces it, and then draws another marble. what is p(red then blue then green)?\n$\frac{1}{64}$\n$\frac{1}{32}$\n$\frac{1}{2}$\n$\frac{3}{4}$

heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag, replaces it, and then draws another marble. what is p(red then blue then green)?\n$\frac{1}{64}$\n$\frac{1}{32}$\n$\frac{1}{2}$\n$\frac{3}{4}$

Answer

Explanation:

Step1: Calculate probability of red

There is 1 red marble out of 4 marbles. So the probability of drawing a red marble $P(\text{red})=\frac{1}{4}$.

Step2: Calculate probability of blue

Since the marble is replaced, there is 1 blue marble out of 4 marbles. So the probability of drawing a blue marble $P(\text{blue})=\frac{1}{4}$.

Step3: Calculate probability of green

Since the marble is replaced, there are 2 green marbles out of 4 marbles. So the probability of drawing a green marble $P(\text{green})=\frac{2}{4}=\frac{1}{2}$.

Step4: Calculate combined probability

For independent - events (because of replacement), the probability of the combined event is the product of the individual probabilities. So $P(\text{red then blue then green})=P(\text{red})\times P(\text{blue})\times P(\text{green})=\frac{1}{4}\times\frac{1}{4}\times\frac{1}{2}=\frac{1}{32}$.

Answer:

$\frac{1}{32}$