The probability that Jennifer rolls an even number from fair die and pulls a black chip from the bag is 1/6.
What is the chain rule in probability for two events?
For two events, A and B:
The chain rule states that the probability that A and B both occur is given by:
\(P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)\)
Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:
\(P(A \cap B) = P(A)P(B)\)
It is because
\(P(A \cap B) = P(A)P(B)\)
Therefore, using chain rule and above facts gives:
\(P(A \cap B) = P(A)P(B)\)
Jennifer has a bag of chips that contains 2 red chips and 1 black chips. Total chips in the bag is 3. Thus, the probability of pulls a black chip from the bag is,
\(P(A)=\dfrac{1}{3}\)
Jennifer also has a fair die. A fair die has 6 number of total outcome and 3 even number outcome(2,4,6). Thus, the probability that she rolls an even number is,
\(P(B)=\dfrac{3}{6}\\P(B)=\dfrac{1}{2}\)
Thus, the probability of rolls an even number and pulls a black chip from the chain rule is,
\(P(A \cap B) = P(A)P(B)\\P(A \cap B) = \dfrac{1}{3}\times\dfrac{1}{2}\\P(A \cap B) = \dfrac{1}{6}\)
Thus, the probability that Jennifer rolls an even number from fair die and pulls a black chip from the bag is 1/6.
Learn more about the chain rule here;
https://brainly.com/question/11549233
