Question

select the correct answer from the drop - down menu. a coin is biased to display heads 75% of the time. it is tossed 20 times, and the outcomes are recorded. the most improbable simulation for this coin is heads.

Explanation:

Step1: Identify probability of heads and tails

The probability of getting heads $p = 0.75$ and the probability of getting tails $q=1 - p= 1 - 0.75 = 0.25$. The number of trials $n = 20$.

Step2: Recall binomial probability formula

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$. The most - probable number of heads $k$ in $n$ trials of a binomial distribution is around $np$.

Step3: Calculate $np$

$np=20\times0.75 = 15$.

Answer:

15