Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

Solution

Maths sir · 3 steps

Replacement resets the box, so the two draws are independent: just multiply the two probabilities.

1. Count the box. There are 10 + 30 + 20 + 15 = 75 marbles in all. Because each marble goes back, the box has these same 75 marbles for both draws.
2. Each draw. First draw red: P(R) = 10/75 = 2/15. Second draw white: P(W) = 30/75 = 2/5, unaffected by the first draw.

   P(R then W) = 2/15 × 2/5 = 4/75

3. So. The probability that the first marble is red and the second is white is 4/75, option (d).

The idea to keep. With replacement, the box is the same for every draw, so the draws are independent and the probabilities multiply. Without replacement, the counts change before the second draw.

Answer from the NTA final answer key. Solution by PrepWiser.