Theory question 106
ProbabilityIf two fair dice are thrown together twice, find the probability of obtaining a product of six in the first throw and a sum of eight in the second throw.
Show the model answer
Model answer
Product 6: (1,6), (6,1), (2,3), (3,2): P = 4/36 = 1/9.
Sum 8: (2,6), (6,2), (3,5), (5,3), (4,4): P = 5/36.
The throws are independent: P = 1/9 × 5/36 = 5/324.
Explanation
List the outcomes in a 6 × 6 table.