Question

consider a collection of envelopes consisting of 3 red envelopes, 1 blue envelope, 2 green envelopes, and 2 yellow envelopes. if one of the envelopes is selected at random, determine the probability that a red or a blue envelope is selected. the probability of selecting a red or a blue envelope is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of envelopes

Total number of envelopes = \(3 + 1+2 + 2=8\)

Step2: Calculate number of favorable outcomes (red or blue)

Number of red envelopes \(n(R)=3\), number of blue envelopes \(n(B) = 1\). Number of favorable outcomes \(n(R\cup B)=n(R)+n(B)=3 + 1=4\)

Step3: Use probability formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

\(P=\frac{4}{8}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)