The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random from the same jar is 1/3. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?
Answers
SOLUTION :
Given : Probability of selecting green marbles = ¼
Probability of selecting a white marbles = ⅓
Number of yellow marbles in a jar = 10
As we know that , the sum of all the probabilities of all possible outcomes of experiment is 1.
P(green marble) + P(white marble) + P(yellow marble) = 1
¼ + ⅓ + P(yellow marble) = 1
(3 + 4)/12 + P(yellow marble) = 1
7/12 + P(yellow marble) = 1
P(yellow marble) = 1 - 7/12
P(yellow marble) = (12 - 7)/12 = 5/12
P(yellow marble) = 5/12
Probability = Number of favourable outcomes / total number of outcomes
P(yellow marble) = Number yellow marbles / Total number of marbles
5/12 = 10 / Total number of marbles
Total number of marbles = (10 × 12)/5 = 2 ×12 = 24
Total number of marbles = 24
Hence, the total number of marbles in the jar is 24
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Let the total number of marbles in the jar be x.
Now the probabilit of selecting a green marble = Number of green marbles/Total no. of marbles = 1/4 (Given)
So number of green marbles = Total no of marbles / 4 = x/4 (1)
Probability of selecting a white marble = No. of white marbles / Total no. of marbles = 1/3 (Given)
So the no of white marbles = x/3
Now we know that the total probability should be 1.
Hence the probability of selecting a yellow marble should be = 1- (Probability of selecting a white marble + Probability of selecting a green marble)
So the probability of selecting a yellow marble = 1-(1/4+ 1/3 ) = 1-(7/12) = 5/12 (3)
But if we calculate the probability of Selecting a yellow marble if should be : No of yellow marbles/ Total no. of marbles = 10/ x
But 10/x Should be equal to Equation (3)
So 5/12 = 10/x
So x = 24.
Hence the total no. of marbles = 24.