First slide

Theorems of probability

Question

Two numbers are selected randomly from the set S = {1,2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4is

Moderate

A

$\frac{1}{15}$
B

$\frac{14}{15}$
C

$\frac{1}{5}$
D

$\frac{4}{5}$

Solution

The minimum of two numbers will be less than 4 or at least one of the numbers is less than 4.
Therefore,
$\begin{matrix} P (at least one numbers < 4) = 1 - P (both the numbers \geq 4) \\ = 1 - \frac{3}{6} \times \frac{2}{5} \\ = 1 - \frac{6}{30} \\ = 1 - \frac{1}{5} = \frac{4}{5} \end{matrix}$

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