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  • A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If probability of at least 4 successes is <img alt="\frac{\mathrm{k}}{3^{11}}" src="https://entrancecorner.on

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If probability of at least 4 successes is \frac{\mathrm{k}}{3^{11}}, then k is equal to :

Option: 1

164


Option: 2

 123


Option: 3

82


Option: 4

75


Answers (1)

best_answer

n(\text { total } 5)=\{1,4),(2,3),(3,2),(4,1)\}=4

\mathrm{P}($ success $)=\frac{4}{36}=\frac{1}{9}
\mathrm{P}( \text{at least 4 success} )=\mathrm{P}(4 \, success )+\mathrm{P}(5 \, success)

={ }^{5} \mathrm{C}_{4} \cdot\left(\frac{1}{9}\right)^{4} \cdot \frac{8}{9}+{ }^{5} \mathrm{C}_{5}\left(\frac{1}{9}\right)^{5}=\frac{41}{9^{5}}=\frac{41}{3^{10}}=\frac{123}{3^{11}}=\frac{\mathrm{k}}{3^{11}}
\mathrm{K}=123
 

Posted by

himanshu.meshram

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