First slide

Random variable and probability distribution

Question

$A p a i r o f f a i r d i c e i s t h r o w n i n d e p e n d e n t l y t h r e e t i m e s t h e p r o b a b i l i t y o f g e t t i n g a s c o r e o f 9 e x a c t l y t w i c e i s$

Moderate

A

$\frac{8}{9}$
B

$\frac{8}{729}$
C

$\frac{8}{243}$
D

$\frac{1}{1729}$

Solution

$In a single throw 9 occurs as (3, 6), (4, 5), (5, 4), (6, 3)$
$The probability p = \frac{4}{36} = \frac{1}{9}$
$The probability of getting 9 twice is = 3 C_{2} p^{2} (1 - p) = \frac{8}{243}$

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