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Probability Part 2

Section: Mathematics

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Question : 43 of 100

Marks: +1, -0

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{k}{3^{11}}

k

[6-Apr-2023 shift 1]

164
123
82
75

Solution:

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

\;P(\text{ success })=\;\frac{4}{36}=\;\frac{1}{9}

\;P(\text{ at least }\;4\;\text{ success })=P(4\;\text{ success })+P(5\;\text{ success })

\;= {}^{5}C_{4} \cdot \left(\frac{1}{9}\right) \cdot \frac{8}{9}+ {}^{5}C_{5} \left(\frac{1}{9}\right)^5=\;\frac{41}{9^5}=\;\frac{41}{3^{10}}=\;\frac{123}{3^{11}}=\;\frac{k}{3^{11}}

\;K=123

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