consider a jar containing 20 marbles. there are 5 red, 3 green, 2 yellow with stripes, 7 blue, and 3 green…

Explanation:

Step1: Calculate number of green marbles

There are 3 non - striped green and 3 striped green marbles. So total green marbles $n(G)=3 + 3=6$.

Step2: Calculate number of striped marbles

There are 2 yellow striped and 3 green striped marbles. So total striped marbles $n(S)=2 + 3=5$.

Step3: Calculate number of green and striped marbles

The number of marbles that are both green and striped $n(G\cap S) = 3$.

Step4: Use the addition rule of probability

The formula for $P(G\cup S)$ is $P(G\cup S)=\frac{n(G)+n(S)-n(G\cap S)}{n(T)}$, where $n(T) = 20$ (total number of marbles). Substitute the values: $n(G)=6$, $n(S)=5$, $n(G\cap S)=3$ and $n(T)=20$ into the formula. $P(G\cup S)=\frac{6 + 5-3}{20}=\frac{8}{20}$.

Step5: Simplify the fraction

$\frac{8}{20}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$