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**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Probability**

**Exam Question:**

A black as well as a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

**Answer:**

For GCSE Mathematics, you should know:

Let E represent getting an **8 **on both dice, and let F represent the red die producing a value that is **less than 4**.

*E:(2,6),(3,5),(4,4),(5,3),(6,2)*

*P(E)= 5/36*

*F:(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)*

P(F)= 18/36 =12

P(E∩F)=2/36

As such, P(E/F) = P(E∩F)/P(F) x (2/36)/(1/2) = 1/9

Work hard for your GCSE Mathematics examination!

End of analysis. Great!