Q) A bag contains 30 balls out of which ’m’ number of balls are blue in colour.
(i) Find the probability that a ball drawn at random from the bag is not blue.
(ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 5/4 times the probability of drawing a blue ball in the first case. Find the value of m.

(Q 29 – 30/4/2 – CBSE 2026 Question Paper)

Ans:

(i) Probability of NOT drawing a blue ball:

Step 1: Since, the bag has total 30 balls, and each ball has equal chance of being drawn,

∴ total outcomes of drawing 1 ball at a time = 30

Step 2: Now, the bag has m number of blue balls

∴ Each blue ball has equal chance of being drawn

∴ The favorable outcomes of drawing a blue ball = m

Step 3: Since the probability =

∴ Probability of drawing a blue ball in 1st case, P_B1 =

Step 4: ∵ Probability of an event happening + Probability of an event NOT happening = 1

∴ Probability of an event NOT happening = 1 – Probability of an event happening

Similarly, Probability of NOT drawing a blue ball in 1st case, PB’

= 1 – probability of drawing a blue ball = 1 – P_B1

= 1 – =

Therefore, the probability of NOT drawing a blue ball is

(ii) Value of m:

Step 5: If 6 more blue balls are added in the bag,

then total balls in the bag = 30 + 6 =36

∴ total outcomes of drawing one ball at a time = 36

Step 6: Revised number of blue balls in the bag = (m + 6)

∴ the favorable outcomes of drawing a blue ball = (m + 6)

Step 7: ∴ Probability of drawing a blue ball in case 2, P_B2

=

=

Step 8: By given condition “probability of drawing a blue ball will be 5/4 times the probability of drawing a blue ball in the first case”

∴ P_B2 = x P_B1

∴

∴

∴ 24 (m + 6) = 36 m

∴ 24 m + 144 = 36 m

∴ 36 m – 24 m = 144

∴ 12 m = 144

∴ m = = 12

Therefore, the value of m is 12.

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