Question

You are stuck at home watching people walk down the street. Assuming half the people are wearing black shoes, 1/3 are wearing white shows and 1/6 are wearing red shoes. What is the probability that you will see a person wearing black shoes before you see a person wearing white ones

Answer 1

Answer:

The probability of seeing a person wearing black shoes before seeing a person wearing white ones = 60%

Step-by-step explanation:

People watched walking down the street = 100%

People wearing black shoes = 1/2 = 50%

People wearing white shoes = 1/3 = 33.33%

People wearing red shoes = 1/6 = 16.67%

Probability of black shoes to white shoes = percentage of persons wearing black shoes/sum of the percentages of people wearing black and white shoes)

= 50% : 33.33%

= 60% (50%/83.33%)

When expressed in ratio terms, it means that you will see 1.5 (50%/33.33% or 1.5 : 1) persons wearing black shoes before you see a person wearing white shoes.

Answer 2

The probability of an event is how likely the event is to happen. The probability that you will see a person wearing black shoes before seeing a person wearing white ones is 0.60

Given that:

$P(B) = 0.5$ --- half wears black

$P(W) = 1/3$ --- those wearing white

$P(R) = 1/6$ --- those wearing white

The probability that you will see a person wearing black shoes before seeing a person wearing white ones is represented as:

$P(B|W)$

So, we have:

$P(B|W) = \frac{P(B)}{P(B\ n\ W)}$

Where:

$P(B\ n\ W) = P(B) + P(W) - P(B\ or\ W)$

$P(B\ n\ W) = 0.5 + 1/3 - 0$

$P(B\ n\ W) = 0.83$

So, we have:

$P(B|W) = \frac{P(B)}{P(B\ n\ W)}$

$P(B|W) = \frac{0.50}{0.83}$

$P(B|W) = 0.60$

Hence, the probability that you will see a person wearing black shoes before seeing a person wearing white ones is 0.60

Read more about probabilities at:

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