Multiple choice

A six faced unbiased die is thrown twice and sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is

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

Possible pairs summing to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Total 6 outcomes. Outcomes with at least one 3 are (3,4) and (4,3). Probability = 2/6 = 1/3.

AI explanation

Using the conditional probability formula, we find the probability as P(number 3 appeared at least once and sum is 7) divided by P(sum is 7). When a die is thrown twice, the sample space for a sum of 7 consists of 6 outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The outcomes where the number 3 appears at least once are (3,4) and (4,3). Therefore, the required probability is 2 divided by 6, which equals 1/3.

Keep practicing — related questions