Multiple choice

A box contains 'a' white and 'b' black balls. 'c' balls are drawn at random with replacement. The expected number of black balls drawn is

  1. $\displaystyle \frac{a}{a+b}$
  2. $\displaystyle \frac{ac}{a+b}$
  3. $\displaystyle \frac{bc}{a+b}$
  4. $\displaystyle \frac{c}{a+b}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a black ball in one trial is b / (a + b). For c trials with replacement, the expected number is c times the probability of success in a single trial, which is c * (b / (a + b)).

AI explanation

This scenario represents a binomial distribution where the expected value is given by the formula E(X) = n * p. The probability of drawing a black ball is b/(a + b). Multiplying the number of trials c by this probability gives the expected number of black balls as bc/(a + b).

Keep practicing — related questions