for example, 12 marbles are red and made of plastic. the table also gives totals for each category. for…
for example, 12 marbles are red and made of plastic. the table also gives totals for each category. for example, 38 marbles are red. suppose a marble is drawn at random. a) what is the probability that marble is red and made of plastic? b) what is the probability that marble is red? c) what is the probability that marble is made of plastic? d) what is the probability that marble is red or made of plastic? e) what is the probability that marble is not red?
Answer
Explanation:
Step1: Recall probability formula
Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of marbles is 84.
Step2: Calculate probability for part d
Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event that the marble is red and $B$ is the event that the marble is plastic. $P(A)=\frac{38}{84}$, $P(B)=\frac{28}{84}$, $P(A\cap B)=\frac{12}{84}$. $P(A\cup B)=\frac{38 + 28- 12}{84}=\frac{54}{84}=\frac{9}{14}$.
Step3: Calculate probability for part e
The probability that a marble is not red is $1 - P(\text{Red})$. Since $P(\text{Red})=\frac{38}{84}$, then $P(\text{not Red})=1-\frac{38}{84}=\frac{84 - 38}{84}=\frac{46}{84}=\frac{23}{42}$.
Answer:
d) $\frac{9}{14}$ e) $\frac{23}{42}$