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In recent days, Rudy has worn a brown shirt on $5$ days and shirts in other colors on $5$ days. Considering this data, how many times would you expect Rudy to wear a brown shirt in the next $12$ days? $\newline$ ____ times $\newline$

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Full solution

Q. In recent days, Rudy has worn a brown shirt on

5

days and shirts in other colors on

5

days. Considering this data, how many times would you expect Rudy to wear a brown shirt in the next

12

days?

\newline

____ times

\newline

Calculate Total Days: Step $1$ : Calculate the total number of days Rudy wore shirts. $\newline$ Total days $= \text{Days with brown shirts} + \text{Days with other color shirts}$ $\newline$ Total days $= 5 + 5 = 10$
Determine Probability: Step $2$ : Determine the probability that Rudy wears a brown shirt. $\newline$ Probability $P$ of wearing a brown shirt = Number of days with brown shirts / Total number of days $\newline$ $P(\text{brown shirt}) = \frac{5}{10} = 0.5$
Calculate Expected Days: Step $3$ : Calculate the expected number of days Rudy will wear a brown shirt in the next $12$ days. $\newline$ Expected days = Probability of brown shirt $\times$ Number of upcoming days $\newline$ Expected days = $0.5 \times 12 = 6$

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