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

Question

Philoid · Accepted Answer

When a dice is thrown 2 times, total outcomes are

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

= 36 possible outcomes

A= sum of numbers is 6

={(1,5),(2,4),(3,3),(4,2),(5,1)} = 5

P(A) =

B= 4 has appeared ateast once

= {(1,4),(2,4),(3,4),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,4),(6,4)} =11

P(B)=

(A ∩ B) = sum of two number is 6 and also 4 has occurred ateast once

(A ∩ B) ={ (2,4),(4,2)} = 2

P(A ∩ B) =

Conditional probability = = (answer)