A box contains 5 red, 7 blue, and 8 yellow marbles. Two marbles are drawn successively without replacement. Find the probability that the second marble is blue given that the first marble drawn is red.

medium 2 marks Class 12 · Mathematics · Probability

Answer

\frac{7}{19}

The correct answer is $\frac{7}{19}$ — Conditional probability $P (second blue ∣ first red) = \frac{7}{19}$ .

Step-by-step solution

State the given condition: the first marble drawn is red.
After removing one red marble, the remaining marbles are 4 red, 7 blue, 8 yellow, total $4 + 7 + 8 = 19$ .
The required event is that the second marble is blue, so the favourable count is 7.
Conditional probability $P (second blue ∣ first red) = \frac{7}{19}$ .

Common mistake: Using the original total of 20 marbles instead of 19 after the first draw.

Concept tested: Conditional probability without replacement