March 15, 2023
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!