Question

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.

Answer 1

The probability that a randomly selected contestant has a grey beard or is only in the beard competition is 1.

Step-by-step explanation:

To find the probability that a randomly selected contestant has a grey beard or is only in the beard competition, we need to calculate the total number of contestants with a grey beard and those only in the beard competition, and divide it by the total number of contestants.

In this case, there are 4 contestants with a grey beard and 10 contestants only in the beard competition. The total number of contestants is 10.

If a contestant can't be both in the mustache competition and in the beard competition only at the same time, we can add the number of contestants to get the total number of contestants in either category. Thus, 4 + 10 = 14 is the total number of contestants. So, the probability is (4 + 10) / 14 = 14/14 = 1.

Answer 2

Step 1: Write out the formula

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

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,

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

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