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Q.
A fair die is rolled six times. The probability of rolling "five or six" atleast five times is
Probability - Part 2
Solution:
$P ( S )= P = P (5$ or 6$)=\frac{1}{3}$
$P ( F )= q =\frac{2}{3} ; n =6$
$P \text { (atleast } 5 \text { successes) } = P (5)+ P (6)={ }^6 C _5\left(\frac{1}{3}\right)^5\left(\frac{2}{3}\right)+{ }^6 C _6\left(\frac{1}{3}\right)^6 $
$=\left(\frac{1}{3}\right)^6[12+1]=\frac{13}{729} $