Question

Bag A contains 'P green and 18 yellow balls while bag B contains (P+2) green balls and 22 more number of yellow balls than that of in bag A. Probability of selecting a green ball from bag A is 1/12 more than probability of selecting a green ball from bag B. Find total number of balls in bag B. ( P 50)

Answer 1

Answer:

22

Step-by-step explanation:

22

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Answer 2

Answer:

The number of balls in bag B is 240 or 48

Step-by-step explanation:

We know,

Probability of an event = Number of favorable outcomes/ Total number of outcomes

Given,

Bag A contains 'P' green and 18 yellow balls

Bag B contains  'P+2' green  and  18+22 yellow balls

Probability of selecting a green ball from bag A= $\frac{1}{12}$ + probability of selecting a green ball from bag B

Required to find the total number of balls in Bag B

total number of balls in Bag B = P+2 +18+22 = P+42

Let $P_1$ and $P_2$ be the probability of selecting green balls from Bag A and Bag B respectively

Then

Then, $P_1$  = $P_2$ + $\frac{1}{12}$  ----------------------(1)

Probability of selecting a green ball from bag A = $P_1$ =

$\frac{no. of green balls in bag A}{Total no. of balls in bag A} = \frac{P}{P+18}$

Probability of selecting a green ball from bag B = $P_2$ =

$\frac{no. of green balls in bag B}{Total no. of balls in bag B} = \frac{P+2}{P+2+18+22} = \frac{P+2}{P+42}$

Substituting the value of $P_1$ and $P_2$ in equation (1)

$\frac{P}{P + 18} = \frac{1}{12} + \frac{P+2}{P +42}$

LCM =  12(P+42)

$\frac{P}{P + 18} = \frac{P+42 + 12(P +2)}{12(P+42)}$

$\frac{P}{P + 18} = \frac{13P+66 }{12P+504}$

P(12P+504) = (13P+66)(P+18)

$12P^{2} + 504 P = 13P^2 + 234P +66P + 1188$

Rearranging we get,

$P^2 - 204 P +1188 = 0$

To factorize the above equation we need to find two numbers such that Sum = -204 and Product 1188

Two such numbers are (-198) and (-6)

Then we have,

$P^2 - 198 P - 6P +1188 = 0$

(P-198)(P - 6) = 0

P = 198 or P = 6

Then Total number of balls in Bag B = P+42 = 198 +42 OR 6+42

= 240 OR 48

Hence Total number of balls in Bag B = 240 or 48