Question

marbles table

	blue	red	green	total
steel	11	13	3	27
plastic	12	20	0	32
total	24	39	18	81

1. fill in the blank 3 points

determine p(glass). (enter as fraction.)
find p(glass | green).
did the condition of being green increase/decrease the likelihood of drawing a glass marble? choose your answer...

1. fill in the blank 3 points

determine p(red). (enter as fraction.)
find p(red | steel).
did the condition of being green increase/decrease the likelihood of drawing a glass marble? choose your answer...

Explanation:

Step1: Recall probability formula

The probability of an event $A$ is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate $P(\text{glass})$

The total number of marbles is $81$. The number of glass marbles is $22$. So $P(\text{glass})=\frac{22}{81}$.

Step3: Calculate $P(\text{glass}|\text{green})$

The number of green marbles is $18$, and the number of green - glass marbles is $15$. So $P(\text{glass}|\text{green})=\frac{15}{18}=\frac{5}{6}$. Since $\frac{5}{6}\approx0.833>\frac{22}{81}\approx0.272$, the condition of being green increases the likelihood of drawing a glass marble.

Step4: Calculate $P(\text{red})$

The number of red marbles is $39$. So $P(\text{red})=\frac{39}{81}=\frac{13}{27}$.

Step5: Calculate $P(\text{red}|\text{steel})$

The number of steel marbles is $27$, and the number of red - steel marbles is $13$. So $P(\text{red}|\text{steel})=\frac{13}{27}$. Since $P(\text{red}) = P(\text{red}|\text{steel})=\frac{13}{27}$, the condition of being steel does not change the likelihood of drawing a red marble.

Answer:

1. $P(\text{glass})=\frac{22}{81}$, $P(\text{glass}|\text{green})=\frac{5}{6}$, the condition of being green increases the likelihood of drawing a glass marble.
2. $P(\text{red})=\frac{13}{27}$, $P(\text{red}|\text{steel})=\frac{13}{27}$, the condition of being steel does not change the likelihood of drawing a red marble.