Respuesta :
Find each probability separately and then multiply the two together
Probability for even number is 3/6 or 1/2 because their are 3 even numbers out of 6 numbers
Probability to get a black chip is 1 black chip out of 3 totals so 1/3
Multiply 1/3 by 1/2
Answer 1/6
Probability for even number is 3/6 or 1/2 because their are 3 even numbers out of 6 numbers
Probability to get a black chip is 1 black chip out of 3 totals so 1/3
Multiply 1/3 by 1/2
Answer 1/6
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:
[tex]P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)[/tex]
Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
It is because
[tex]P(A \cap B) = P(A)P(B)[/tex]
Therefore, using chain rule and above facts gives:
[tex]P(A \cap B) = P(A)P(B)[/tex]
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,
[tex]P(A)=\dfrac{1}{3}[/tex]
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,
[tex]P(B)=\dfrac{3}{6}\\P(B)=\dfrac{1}{2}[/tex]
Thus, the probability of rolls an even number and pulls a black chip from the chain rule is,
[tex]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}[/tex]
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
