The total probability of choosing a green marble not replacing it and then choosing a red marble is [tex]\frac{1}{12}[/tex]
Solution:
Given that bag contains one red one yellow one blue and one green marble
To find: Probability of choosing a green marble not replacing it and then choosing a red marble
The probability of an event is given as:
[tex]\text{ probability } =\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}$[/tex]
Here total number of possible outcomes = 1 red + 1 yellow + 1 blue + 1 green
total number of possible outcomes = 4 marbles
Here favourable outcome is choosing a green marble not replacing it and then choosing a red marble
Let us first find probability of choosing a green marble
Favorable outcome = green marble
Number of favorable outcomes = 1
[tex]probability = \frac{1}{4}[/tex]
Now without replacing, we have to choose a red marble
Without replacing means, green marble is not considered
So total number of possible outcomes = 4 - 1 = 3
[tex]probability = \frac{1}{3}[/tex]
The total probability of choosing a green marble not replacing it and then choosing a red marble:
[tex]\rightarrow \frac{1}{4} \times \frac{1}{3} = \frac{1}{12}[/tex]
So the required probability is [tex]\frac{1}{12}[/tex]
