Multiple choice

A die is thrown $5$ times. If getting an odd number is a success, then what is the probability of getting atleast $4$ successes?

  1. $\cfrac{4}{5}$
  2. $\cfrac{7}{16}$
  3. $\cfrac{3}{16}$
  4. $\cfrac{3}{20}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of odd number (success) p = 1/2. n = 5. P(X >= 4) = P(X=4) + P(X=5). P(X=4) = 5C4 * (1/2)^5 = 5/32. P(X=5) = 5C5 * (1/2)^5 = 1/32. Total = 6/32 = 3/16.

AI explanation

The probability of getting an odd number (a success) on a single die roll is 3/6, or 1/2. Using the binomial probability formula for getting at least 4 successes in 5 trials, we add the probabilities of exactly 4 and exactly 5 successes. This becomes 5C4 times (1/2)^4 times (1/2) plus 5C5 times (1/2)^5, which equals 5/32 + 1/32, resulting in 6/32 or 3/16.

Keep practicing — related questions