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प्रश्न
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?
उत्तर
Let the no. of green marbles = x
The no. of white marbles = y
No. of yellow marbles = 10
Total no. of possible outcomes = x + y + 10 (total no. of marbles)
Probability P(E) =`"No.of favorable outcomes"/"Total no.of possible outcomes"`
Probability (green marble) =1/4 = `x/(x+y+10)`
⇒ x + y + 10 = 4x
⇒ 3x – y – 10 = 0 …..(i)
Probability (white marble) =1/3 = `y/(x+y+10)`
⇒ x + y 10 = 3y
⇒ x – 2y + 10 = 0 ….(ii)
⇒ 3x – 6y + 30 = 0 ….(iii)
Multiplying by 3,
Sub (i) from (iii), we get
−6y + y + 30 + 10 = 0
⇒ −5y + 40 = 0
⇒ 5y = 40
⇒ y = 8
Subs. Y in (i), 3x – 8 – 10 = 0
3x – 18 = 0
x = 8/3 = 6
Total no. of marbles in jar = x + y + 10 = 6 + 8 + 10 = 24
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