First slide

Theorems of probability

Question

$T h r e e p e o p l e e a c h f l i p t w o f a i r c o i n s . T h e p r o b a b i l i t y t h a t e x a c t l y t w o o f t h e p e o p l e f l i p p e d o n e h e a d a n d o n e t a i l, i s -$

Moderate

A

$\frac{1}{2}$
B

$\frac{3}{8}$
C

$\frac{5}{8}$
D

$\frac{3}{4}$

Solution

$\begin{array}{l} n = 3, P (success) = P (HT or TH) = 1 / 2 \\ \Rightarrow p = q = \frac{1}{2} and r = 2 \\ P (r = 2) =^{3} C_{2} {(\frac{1}{2})}^{2} \cdot \frac{1}{2} = \frac{3}{8} \end{array}$

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