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Out of the people who have already taken their seats at a seminar, $2$ people have black hair while $2$ people do not. Considering this data, how many of the next $16$ people to take their seats should you expect to be black-haired? $\newline$ ____ black-haired people $\newline$

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Q. Out of the people who have already taken their seats at a seminar,

2

people have black hair while

2

people do not. Considering this data, how many of the next

16

people to take their seats should you expect to be black-haired?

\newline

____ black-haired people

\newline

Calculate Total Number: Step $1$ : Calculate the total number of people who have already taken their seats. $\newline$ People with black hair: $2$ $\newline$ People with other hair colors: $2$ $\newline$ Total number of people seated = $2 + 2 = 4$
Determine Probability of Black Hair: Step $2$ : Determine the probability of a person having black hair. $\newline$ Number of people with black hair $= 2$ $\newline$ Total number of people seated $= 4$ $\newline$ Probability ( $P$ ) of black hair $=$ Number of black hair $/$ Total number of people $\newline$ $P(\text{black hair}) = \frac{2}{4} = \frac{1}{2}$
Calculate Expected Number: Step $3$ : Calculate the expected number of black-haired people among the next $16$ attendees. $\newline$ Probability of black hair = $\frac{1}{2}$ $\newline$ Number of new attendees = $16$ $\newline$ Expected number of black-haired attendees = Probability of black hair $\times$ Number of new attendees $\newline$ Expected black-haired = $\frac{1}{2} \times 16 = 8$

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