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Roxanne was the lucky journalist assigned to cover the Best Beard Competition. She recorded the contestants' beard colors in her notepad. Roxanne also noted if the contestants were signed up for the mustache competition later in the day. Only in the beard competition Also in the mustache competition Red beard 3 3 Grey beard 4 2 Brown beard 1 3 What is the probability that a randomly selected contestant has a grey beard or is only in the beard competition? Simplify any fractions.

Respuesta :

Step 1: Write out the formula

[tex]P(M\text{ or G) = P(M) + P(G) - P(M}\cap G)[/tex][tex]\begin{gathered} \text{where } \\ M\text{ and G are events} \end{gathered}[/tex]

Step 2: Write out the given values and substitute them into the formula

Let M be the event for Mustache competition

Let G be the event for Grey Beard

n(M) = 3 + 2 + 3 = 8

n(G) = 4 + 2 = 6

n(GnM) = 4

n(U) = 16

Therefore,

[tex]P(M)=\frac{8}{16},P(G)=\frac{6}{16},P(M\cap G)=\frac{4}{16}[/tex][tex]\begin{gathered} P(M\text{ or G) = }\frac{8}{16}+\frac{6}{16}-\frac{4}{16} \\ =\frac{8+6-4}{16}=\frac{10}{16}=\frac{5}{8} \end{gathered}[/tex]

Therefore, the probability that a randomly selected contestant has a grey beard or is only in the beard competition is 5/8

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