CUET · MATHS · PYQ PAPER 2023
A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then the probability of at least 3 successes is :
- A \(46\left(\frac{1}{6}\right)^4\)
- B \(96\left(\frac{1}{6}\right)^4\)
- C \(625\left(\frac{1}{6}\right)^4\)
- D \(1250\left(\frac{1}{6}\right)^4\)
Answer & Solution
Correct Answer
(A) \(46\left(\frac{1}{6}\right)^4\)
Step-by-step Solution
Detailed explanation
\(p = \frac{6}{36} = \frac{1}{6}\) \(q = 1 - p = \frac{5}{6}\) \(P(X=k) = \binom{n}{k} p^k q^{n-k}\) \(P(X=3) = \binom{5}{3} \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^2 = 10 \cdot \frac{1}{216} \cdot \frac{25}{36} = \frac{250}{6^5}\)…
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