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ICSE Class 10 Mathematics Question 28 of 28

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Question 77

The probability of selecting a blue marble and a red marble from a bag containing red, blue and green marbles is 13\dfrac{1}{3} and 15\dfrac{1}{5} respectively. If the bag contains 14 green marbles, then find :

(a) number of red marbles.

(b) total number of marbles in the bag.

Answer

As the bag contains red, blue and green marbles.

∴ Probability of selecting a red marble + Probability of selecting a blue marble + Probability of selecting a green marble = 1

⇒ 13+15\dfrac{1}{3} + \dfrac{1}{5} + Probability of selecting a green marble = 1

⇒ 5+315\dfrac{5 + 3}{15} + Probability of selecting a green marble = 1

⇒ Probability of selecting a green marble = 1−8151 - \dfrac{8}{15}

⇒ Probability of selecting a green marble = 15−815\dfrac{15 - 8}{15}

⇒ Probability of selecting a green marble = 715\dfrac{7}{15}.

∴No. of green marblesTotal no. of marbles=715⇒14Total no. of marbles=715⇒Total no. of marbles=15×147=30.\therefore \dfrac{\text{No. of green marbles}}{\text{Total no. of marbles}} = \dfrac{7}{15} \\[1em] \Rightarrow \dfrac{14}{\text{Total no. of marbles}} = \dfrac{7}{15} \\[1em] \Rightarrow \text{Total no. of marbles} = \dfrac{15 \times 14}{7} = 30.

(a) Given,

⇒ Probability of selecting a red marble = 15\dfrac{1}{5}.

∴No. of red marblesTotal no. of marbles=15⇒No. of red marbles30=15⇒No. of red marbles=305=6.\therefore \dfrac{\text{No. of red marbles}}{\text{Total no. of marbles}} = \dfrac{1}{5} \\[1em] \Rightarrow \dfrac{\text{No. of red marbles}}{30} = \dfrac{1}{5} \\[1em] \Rightarrow \text{No. of red marbles} = \dfrac{30}{5} = 6.

Hence, no. of red marbles = 6.

(b) Hence, total no. of marbles in the bag = 30.