ariel was the lucky journalist assigned to cover the best beard competition. she recorded the contestants…
ariel was the lucky journalist assigned to cover the best beard competition. she recorded the contestants beard colors in her notepad. ariel also noted if the contestants were signed up for the mustache competition later in the day. what is the probability that a randomly selected contestant is only in the beard competition given that the contestant has a red beard? simplify any fractions.
Answer
Explanation:
Step1: Find total red - bearded contestants
The number of red - bearded contestants is the sum of those only in the beard competition and those also in the mustache competition. So, (4 + 3=7).
Step2: Find red - bearded contestants only in the beard competition
The number of red - bearded contestants only in the beard competition is 4.
Step3: Calculate the conditional probability
The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In this case, the probability that a contestant is only in the beard competition given they have a red beard is (\frac{\text{Number of red - bearded contestants only in the beard competition}}{\text{Total number of red - bearded contestants}}). So the probability is (\frac{4}{7}).
Answer:
(\frac{4}{7})