Question

a person draws a card from a hat. each card is one color, with the following probabilities of being drawn: 1/20 for blue, 1/10 for pink, 1/15 for purple, and 1/25 for black. what is the probability of pulling a pink or purple card, written as a reduced fraction?

Explanation:

Step1: Find the probability of pink and purple

The probability of pink is \( \frac{1}{10} \), and the probability of purple is \( \frac{1}{15} \).

Step2: Use the formula for the probability of the union of two - events

For two mutually - exclusive events \( A \) and \( B \) (a card can't be both pink and purple at the same time), \( P(A\cup B)=P(A)+P(B) \).
So \( P(\text{pink or purple})=\frac{1}{10}+\frac{1}{15} \).

Step3: Find a common denominator

The common denominator of \( 10 \) and \( 15 \) is \( 30 \).
\(\frac{1}{10}+\frac{1}{15}=\frac{1\times3}{10\times3}+\frac{1\times2}{15\times2}=\frac{3}{30}+\frac{2}{30}\).

Step4: Add the fractions

\(\frac{3 + 2}{30}=\frac{5}{30}\).

Step5: Simplify the fraction

Divide both the numerator and denominator by \( 5 \), \(\frac{5\div5}{30\div5}=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)