select the correct answer from the drop - down menu. a coin is flipped 36 times. the least likely result for…
select the correct answer from the drop - down menu. a coin is flipped 36 times. the least likely result for the coin to land on heads is times.
Answer
Answer:
30
Explanation:
Step1: Recall binomial probability concept
For a fair - coin flip (probability of heads $p = 0.5$), $n=36$ flips follow a binomial distribution $X\sim B(n = 36,p = 0.5)$. The probability mass function is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$.
Step2: Analyze the symmetry of binomial distribution
When $p = 0.5$, the binomial distribution $B(n,p)$ is symmetric about $k=\frac{n}{2}$. Here, $n = 36$, so the distribution is symmetric about $k=\frac{36}{2}=18$.
Step3: Determine the least - likely value
The values of $k$ that are farthest from the mean $\mu=np=36\times0.5 = 18$ are the least likely. Among 20, 16, 18, and 30, 30 is the farthest from 18. So the least likely result for the coin to land on heads is 30 times.