Probabilities: 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 [tex]P(c)=\frac{1}{4}[/tex]

[tex]\frac{3}{4}[/tex]

[tex]\frac{1}{4}[/tex]

[tex]\frac{3}{5}[/tex]

[tex]\frac{1}{3}[/tex]

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?

$\frac{32}{36}$

$\frac{20}{36}$

$\frac{30}{36}$

$\frac{1}{8}$

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.

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{5}$

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.

$\frac{1}{14}$

$\frac{1}{15}$

$\frac{1}{9}$

$\frac{1}{18}$