JEE Mains · Maths · STD 11 - 14. probability
Two dice are thrown \(5\) times, and each time the sum of the numbers obtained being \(5\) is considered a success. If the probability of having at least \(4\) successes is \(\frac{\mathrm{k}}{3^{11}}\), then \(\mathrm{k}\) is equal to
- A \(82\)
- B \(123\)
- C \(164\)
- D \(75\)
Answer & Solution
Correct Answer
(B) \(123\)
Step-by-step Solution
Detailed explanation
Probability of success \(=\frac{1}{9}=p\) Probability of failure \(q =\frac{8}{9}\) \(P (\text { at least } 4 \text { success })= P (4 \text { success })+ P (5 \text { success })\) \(={ }^5 C _4 p ^4 q +{ }^5 C _5 p ^5=\frac{41}{3^{10}}=\frac{123}{3^{11}}\) \(k =123\)
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