Answer:
P(W) and P(B) are independent events.
Step-by-step explanation:
Given : A bag contains 5 white marbles and 5 blue marbles. You randomly select one marble from the bag and put it back. Then, you randomly select another marble from the bag.
To find : Which calculation proves that randomly selecting a white marble the first time and a blue marble the second time are two independent events?
Solution :
Independent events - When the probability that one event occurs in no way affects the probability of the other event occurring.
We have given, 5 white marbles and 5 blue marbles.
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
Total number of outcomes = 5+5=10
The probability that a white marble the first time,
[tex]P(W)=\frac{5}{10}= \frac{1}{2}[/tex]
Their is a replacement occurs,
The probability that a blue marble the second time,
[tex]P(B)=\frac{5}{10}= \frac{1}{2}[/tex]
The probability of occurrence of a Blue marble is not affected by occurrence of the probability that we get white marble in first attempt.
Hence, P(W) and P(B) are independent events.
