Question

A bag contains red, white and blue marbles. The probability of selecting a red marble is \[\dfrac{2}{5}\] and that of selecting a blue marble is \[\dfrac{4}{{15}}\]. The probability of selecting a white marble is
(A).\[\dfrac{{13}}{{15}}\]
(B).\[\dfrac{{11}}{{15}}\]
(C).\[\dfrac{3}{5}\]
(D).\[\dfrac{2}{5}\]

Answer 1

Hint: As you know probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we talk about the probability of it occurring. A probability distribution is a collection of probabilities that defines the possibility of observing all of the various outcomes of an event. The sum of the probabilities in a probability distribution is always 1. We have to apply this as our solution.

Complete step by step solution:
The probability of selecting a red marble and a blue marble are given as \[\dfrac{2}{5}\] and \[\dfrac{4}{{15}}\]. As we know,
\[{\text{Probability = }}\dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total number of possible outcomes}}}}\]
For both the red and blue marbles the denominator in the probabilities 15. Thus 15 is the total number of possible outcomes.
We can calculate the number of favourable outcomes for white marble as:
\[
15 - ({\text{favourable outcomes for red and blue marbles)}} \\
\Rightarrow {\text{15 - (2 + 4)}} \\
\Rightarrow {\text{9}} \\
\]
Probability of drawing a white marble is \[\dfrac{9}{{15}}\] or \[\dfrac{3}{5}\].
Another method is applying the set rule that the sum of probabilities in probability distribution is 1.
So, probability of drawing white marble:
\[
1 - (\dfrac{2}{{15}} + \dfrac{4}{{15}}) \\
\Rightarrow 1 - \dfrac{6}{{15}} \\
\Rightarrow \dfrac{{15 - 6}}{{15}} = \dfrac{9}{{15}} = \dfrac{3}{5} \\
\]

Thus, the correct option is (C).

Note: The probability of an event is a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Students can apply either method for calculating the solution. Probability is a very important topic from an exam point of view and also for application in our daily life.