# Q.7 A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Probability of 6 in a throw of die =P

$P=\frac{1}{6}$

$q=1-P=1-\frac{1}{6}=\frac{5}{6}$

Probability that 2 sixes come in first five throw of die :

$=^5C_2 (\frac{5}{6})^3 (\frac{1}{6})^2$

$=\frac{10\times 5^3}{6^5}$

Probability that third six comes in sixth throw :

$=\frac{10\times 5^3}{6^5}\times \frac{1}{6}$

$=\frac{10\times 125}{6^6}$

$=\frac{1250}{23328}$

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