A dice is thrown twice and the sum of the numbers appearing is observed to be 6. The conditional probability that the number 4 has appeared at least once is:

Question

A dice is thrown twice and the sum of the numbers appearing is observed to be 6. The conditional probability that the number 4 has appeared at least once is: (A) 1/5 (B) 4/5 (C) 3/5 (D) 2/5

Tardigrade Admin · Accepted Answer

From the given condition sum of a dice thrown twice is 6.

∴

Number of cases formed is (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5
Since 4 has to occur, and the probability that at least 4 has appeared once is

= \frac{2}{5}

Q. A dice is thrown twice and the sum of the numbers appearing is observed to be 6. The conditional probability that the number 4 has appeared at least once is:

1/5

4/5

3/5

2/5

From the given condition sum of a dice thrown twice is 6. ∴ Number of cases formed is (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 Since 4 has to occur, and the probability that at least 4 has appeared once is =52​

From the given condition sum of a dice thrown twice is 6.
$∴$ Number of cases formed is (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5
Since 4 has to occur, and the probability that at least 4 has appeared once is $= \frac{2}{5}$