First slide

Theorems of probability

Question

Two persons $A, B$ have to speak at a function with 10 other persons. If the persons speak at random order, the probability that $A$ speaks immediately before $B$ is

Easy

A

$\frac{1}{12}$
B

$\frac{1}{3}$
C

$\frac{3}{8}$
D

$\frac{5}{6}$

Solution

$n (S) = 12!, (10 + 2 = 12)$
$n (E) = 11! \times 1 \to {A B}$

$[\begin{matrix} A B - 1 unit \\ 10 - 10 units \end{matrix}]$

The probability that A speaks immediately before B is $P (E) = \frac{11!}{12!} = \frac{1}{12}$

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