Question

if the true probability of heads is 0.5, how many heads would you expect to observe after 50 tosses?
number of heads after 50 tosses:
if the true probability of heads is 0.5, how many heads would you expect to observe after 500 tosses?
number of heads after 500 tosses:

Explanation:

Step1: For 50 tosses

The expected number of heads in a binomial experiment is given by the formula \( E(X)=n\times p \), where \( n \) is the number of trials and \( p \) is the probability of success (getting a head here). Here, \( n = 50 \) and \( p=0.5 \). So we calculate \( 50\times0.5 \).
\( 50\times0.5 = 25 \)

Step2: For 500 tosses

Using the same formula \( E(X)=n\times p \), with \( n = 500 \) and \( p = 0.5 \). We calculate \( 500\times0.5 \).
\( 500\times0.5=250 \)

Answer:

Number of heads after 50 tosses: 25
Number of heads after 500 tosses: 250