JEE Mains · Maths · STD 12 - 13. probability
In a tournament, a team plays \(10\) matches with probabilities of winning and losing each match as \(\frac{1}{3}\) and \(\frac{2}{3}\) respectively. Let \(x\) be the number of matches that the team wins, and \(y\) be the number of matches that team loses. If the probability \(\mathrm{P}(|\mathrm{x}-\mathrm{y}| \leq 2)\) is \(\mathrm{p}\), then \(3^9 \mathrm{p}\) equals ...........
- A \(4215\)
- B \(4548\)
- C \(8288\)
- D \(2456\)
Answer & Solution
Correct Answer
(C) \(8288\)
Step-by-step Solution
Detailed explanation
\( P(W)=\frac{1}{3} \quad P(L)=\frac{2}{3} \) \( x=\text { number of matches that team wins } \) \( y=\text { number of matches that team loses } \) \( |x-y| \leq 2 \text { and } x+y=10 \) \( |x-y|=0,1,2 \quad x, y \in N\) Case \(-I\) : \(|x-y|=0 \Rightarrow x=y \)…
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