Question

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 odd number is 415 . The probability of selecting a black chip is 915

What is the probability of selecting a chip with an odd number given that the chip is black?

Enter your answer, as a simplified fraction, in the boxes.
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Answer 1

The probability of selecting a chip with an odd number given that the chip is black is 20/27.

Step-by-step explanation:

To find the probability of selecting a chip with an odd number given that the chip is black, we need to use conditional probability.

We are given that the probability of selecting a black chip is 9/15 (or 3/5). We are also given that the probability of selecting a black chip with an odd number is 4/15 (or 4/9).

The probability of selecting a chip with an odd number given that the chip is black can be calculated using the formula for conditional probability as:

P(odd | black) = P(odd and black) / P(black)

Substituting the given probabilities, we get:

P(odd | black) = (4/9) / (3/5) = 20/27

Therefore, the probability of selecting a chip with an odd number given that the chip is black is 20/27.

Answer 2

The probability of selecting an odd number given that the chip is black is 0.454.

Step-by-step explanation:

First of all, the value of probability is always less than 1, so the following value of probabilities need to be corrected and are:

Probability of selecting a black chip with an odd number(A)=0.415

Probability of selecting a black chip(B)= 0.915

Probability of A given B is denoted by=P(A | B)

P(A|B) =P(A∩B)/P(B)

P(B)=0.915

P(A∩B)=0.415

P(A|B)=
`(0.415)/(0.915)`

P(A|B)=0.454

The probability of selecting an odd number given that the chip is black is 0.454.