Question

The probability of obtaining at least two 'Six' in throwing a fair dice 4 times is

• A. 425/432
• B. 19/144
• C. 13/144
• D. 125/432

Answer 1

The correct option is B 19/144

Let p be the probability of getting 6
$p=\frac{1}{6}\text{and}q=1-\frac{1}{6}=\frac{5}{6}$

n = 4

P(obtaining at least two six)

$=4C_2{\left(\frac{1}{6}\right)}^2{\left(\frac{5}{6}\right)}^2+4C_3{\left(\frac{1}{6}\right)}^3\left(\frac{5}{6}\right)+4C_4{\left(\frac{1}{6}\right)}^4$

$=\frac{150}{1296}+\frac{20}{1296}+\frac{1}{1296}=\frac{171}{1296}=\frac{19}{144}$