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The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is \[\dfrac{1}{4}\]. The probability of selecting a white marble at random from the same jar is \[\dfrac{1}{3}\]​. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

a) 22
b) 26
c) 28
d) 24

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Last updated date: 15th Jun 2024
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Answer
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Hint:
Probability of the selecting yellow marble is the ratio of the number of yellow marbles and total number of marbles. Probability of the selecting yellow marble can also be calculated by
the difference of total probability and the sum of probability of selecting a white marble and the probability of selecting a green marble.

Complete step by step solution:
Assume that total number of marbles in the jar be x
Given that number of yellow marbles in a jar \[ = 10\]
Given that the probability of selecting a green marble \[ = \dfrac{1}{4}\]
Also, the probability of selecting a white marble\[ = \dfrac{1}{3}\]
We know that the total probability
Hence, Probability of selecting a yellow marble =1–(Probability of
selecting a white marble + Probability of selecting a green marble)
So the probability of selecting a yellow marble
\[ = 1 - \left( {\dfrac{1}{4} + \dfrac{1}{3}} \right) = 1 - \dfrac{7}{{12}} =
\dfrac{5}{{12}}\]----(1)
But the probability of selecting a yellow marble
$= \dfrac{{Number{\text{ of yellow Marbles}}}}{{Total{\text{ no}}{\text{.
of marbles}}}} = \dfrac{{10}}{x} \\
\therefore \dfrac{5}{{12}} = \dfrac{{10}}{x} \text{from (1)} \\
\Rightarrow x = 10 \times \dfrac{12}{5} \\
\Rightarrow x= 2 \times 12 \\
\therefore x = 24$

Hence the total number of marbles =24

Note:
The sum of total probability is 1.
Probability of given event is the ratio of number of given events by total number of events. We can also interpret the probability in terms of percentage. Suppose the probability of something is $0.75$ then we say $75 \%$ of odds are in favor of the occurrence of that event.