Question

A bag contains \[3\] red marbles, \[2\] blue marbles, and \[5\] green marbles. What is the probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble?

Answer 1

Hint: Using the definition of probability, we will first find the probability of randomly selecting a blue marble then we will calculate the probability of randomly selecting a green marble without replacing the blue marble. Then we will multiply both these probabilities to find the probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble.

Complete step-by-step answer:
As we know, Probability of an event \[ = \dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total number of outcomes}}}}\]
In this question, initially we have \[3\] red marbles, \[2\] blue marbles, and \[5\] green marbles.
For the probability of randomly selecting a blue marble, we have
\[ \Rightarrow \] Number of favourable outcomes \[ = 2\]
\[ \Rightarrow \] Total number of outcomes \[ = 3 + 2 + 5\]
\[ = 10\]
\[ \Rightarrow \] Probability of randomly selecting a blue marble \[ = \dfrac{2}{{10}}\]
Now, for randomly selecting a green marble without replacing, we have a total number of outcomes as \[3\] red marbles, \[1\] blue marbles, and \[5\] green marbles. So, we can write
\[ \Rightarrow \] Number of favourable outcomes \[ = 5\]
\[ \Rightarrow \] Total number of outcomes \[ = 3 + 1 + 5\]
\[ = 9\]
\[ \Rightarrow \] Probability of randomly selecting a green marble \[ = \dfrac{5}{9}\]
The probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble is equal to the product of probability of randomly selecting a blue marble then without replacing probability of randomly selecting a green marble i.e.,
\[ \Rightarrow \] The probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble \[ = \dfrac{2}{{10}} \times \dfrac{5}{9}\]
\[ = \dfrac{1}{9}\]
Therefore, the probability of randomly selecting a blue marble, then without replacing it, randomly selecting a green marble is \[\dfrac{1}{9}\].

Note: The probability of an event can only lie between \[0\] and \[1\]. A probability of \[1\] indicates that an event certainly takes place, whereas a probability of \[0\] indicates that an event almost never takes place. We can also write probability as a percentage. Also, note that the sum of probabilities of all possible outcomes is \[1\].