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

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 $1$.