JEE Mains · Maths · STD 12 - 13. probability
A six faced die is biased such that \(3 \times P (\) a prime number \()=6 \times P (\) a composite number \()=2 \times P (1)\).Let \(X\) be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of \(X\) is.
- A \(\frac{3}{11}\)
- B \(\frac{5}{11}\)
- C \(\frac{7}{11}\)
- D \(\frac{8}{11}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{11}\)
Step-by-step Solution
Detailed explanation
Let \(\frac{ P (\text { a prime number })}{2}=\frac{ P (\text { a composite })}{1}=\frac{ P (1)}{3}= k\) So, \(P (\) a prime number \()=2 k\), \(P (\) a composite number \()= k\), \(P (1)=3 k\) \(3 \times 2 k +2 \times k +3 k =1\) \(\Rightarrow k =\frac{1}{11}\) \(P (\) success…
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