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  • 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.

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.

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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}

  

Posted by

seema garhwal

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