A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{7}{64}\)
Three of the six faces are odd, so \(p = \frac{1}{2}\), \(q = \frac{1}{2}\), and the number of successes X is binomial with \(n = 6\).
\( \displaystyle P(X = r) = {}^{6}C_{r}\left(\frac{1}{2}\right)^6 = \frac{{}^{6}C_{r}}{64} \)
“At least 5” means \(X = 5\) or \(X = 6\):
\( \displaystyle P(X \ge 5) = \frac{{}^{6}C_{5} + {}^{6}C_{6}}{64} \)
\( \displaystyle = \frac{6 + 1}{64} = \frac{7}{64} \)
CBSE Applied Mathematics (Class XII):
Binomial Distribution
