Question

1. you randomly choose 2 marbles from a bag with 2 yellow, 2 green, and 2 pink marbles, without replacement. what is the probability of choosing a pink marble first or a green marble second? type your answer as a decimal. use only 2 decimal places

Explanation:

Step1: Calculate total number of marbles

There are $2 + 2+2=6$ marbles.

Step2: Calculate probability of choosing a pink marble first

The probability of choosing a pink marble first, $P(P_1)=\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate probability of not - choosing a pink marble first and a green marble second

The probability of not choosing a pink marble first is $\frac{4}{6}$. Then, the probability of choosing a green marble second given that a pink marble was not chosen first is $\frac{2}{5}$. So the probability of this event is $\frac{4}{6}\times\frac{2}{5}=\frac{8}{30}=\frac{4}{15}$.

Step4: Use the addition rule for non - mutually exclusive events

The probability of choosing a pink marble first or a green marble second is $P = P(P_1)+P(\text{not }P_1\text{ and }G_2)$.
$P=\frac{1}{3}+\frac{4}{15}=\frac{5 + 4}{15}=\frac{9}{15}=0.60$

Answer:

$0.60$