Multiple choice

A box contains $3$ red marbles and $2$ white marbles. A marble is drawn and replaced three times from the box. The probability that exactly one red marble is drawn is

  1. $3/5$
  2. $9/125$
  3. $36/125$
  4. $6/125$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a binomial probability problem: n=3, k=1, p=3/5 (red), q=2/5 (white). P(X=1) = C(3,1) * (3/5)^1 * (2/5)^2 = 3 * (3/5) * (4/25) = 36/125.

AI explanation

The probability of drawing a red marble is 3/5 and a white marble is 2/5. Using the binomial distribution formula for exactly one success, calculate 3C1 * (3/5)^1 * (2/5)^2. This multiplies out to 3 * 3/5 * 4/25, which simplifies to 36/125.

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