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Problems in Probability: Difficult Problems with Solutions

Problem 1
Let S={a, b, c} find the value of P(b') if P(b')=1-P(b), P(a)=2P(b) and P(c)=¼
Answer format: x/y
Problem 2
Suppose we have 5 red balls and 4 black balls and get 5 balls randomly. What's the probability of getting 3 red balls and 2 black balls?
Answer format: x/y
Problem 3
Choose two real number between 0 and 2 at random. Find the probability that the summation of these two numbers is less than 2.

Answer format: x/y
Problem 4
Suppose we have a dice that the probability of odd numbers is 5 times more than even numbers.
Find the probability that dice shows 6.
Answer format: x/y
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