Question

Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show ALL your work AND write your answer as a fraction, decimal, and percent

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for probability

$Probability=\frac{number\text{ of required outcomes}}{number\text{ of total outcomes}}$

STEP 2: Get the probability of Chang wearing the white shirt

$\begin{gathered} number\text{ of required outcomes}=1 \\ number\text{ of expected outcomes}=2 \\ Pr(white\text{ shirt\rparen}=\frac{1}{2} \end{gathered}$

STEP 3: Get the probability of Chang wearing tan pants

$\begin{gathered} number\text{ of tan pants}=1 \\ numbe\text{r of total pants}=2 \\ Pr(tan\text{ pants\rparen}=\frac{1}{2} \end{gathered}$

STEP 4: Get the probability that he wears a white shirt and a tan pant

According to the multiplicative law of probability,

$Pr(A\text{ and B\rparen}=Pr(A)\times Pr(B)$

Therefore, the probability of wearing both outfits is:

$\begin{gathered} Pr(White\text{ shirt and tan pant\rparen}=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ To\text{ decimal}=0.25 \\ \text{To percentage}=0.25\times100=25\% \end{gathered}$

Hence, the probability that he wears a white shirt and a tan pant is:

1/4 as a fraction

0.25 as a decimal

25% as a percent