Probability
Binomial Distribution — At Least k Successes
nta_pyq_2023_apr
Grade 12
Question:
A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $\dfrac{k}{3^{11}}$, then $k$ is equal to
Step-by-Step Solution
Key Concept: $P(\text{success})=\frac{4}{36}=\frac{1}{9}$. $P(X\geq4)=\binom{5}{4}(\frac{1}{9})^4(\frac{8}{9})+\binom{5}{5}(\frac{1}{9})^5=\frac{41}{9^5}$.
$k=123$.
Correct Answer: 4