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An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a black chip with an even number is 12 . The probability of selecting a black chip is 35 . What is the probability of selecting a chip with an even number given that the chip is black?

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Answer:


Step-by-step explanation:

Answer:  The probability of selecting a chip with an even number given that the chip is black = 5/6


Step-by-step explanation:


Let B represents the event of getting black chip,


While E represents the event of getting even chip.


So, according to the question,


It is given, The probability of selecting a black chip with an even number is,




And,  The probability of selecting a black chip is,




Thus, the probability of selecting a chip with an even number given that the chip is black,


( By the conditional property )


⇒


Using conditional probability, it is found that there is a 0.3429 = 34.29% probability of selecting a chip with an even number given that the chip is black.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem:

  • Event A: Black chip.
  • Event B: Even number.

  • The probability of selecting a black chip with an even number is 0.12, hence [tex]P(A \cap B) = 0.12[/tex].
  • The probability of selecting a black chip is 0.35, hence [tex]P(A) = 0.35[/tex]

Then:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.12}{0.35} = 0.3429[/tex]

0.3429 = 34.29% probability of selecting a chip with an even number given that the chip is black.

To learn more about conditional probability, you can take a look at https://brainly.com/question/25790531

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