Question

0 COUNTING AND PROBABLITY -computing conditional probability using a samplo spaco We have a deck of 12 cards numbered from 1 to 12. Some are white and some are grey, as shown below. 6 7 8 9 10 11 12 Answer the following questions. Write each answer as a fraction. A card will be drawn at random (a) What is the probability that the number 9 card is duiwn? What is the probability that the number 9 card is drawn, given that the card drawn is white? (b)

Answer 1

We have a deck of 12 cards numbered from 1 to 12.

There are some white and grey cards.

Probability of each number is $\frac{1}{12}$

There are 6 white and 6 grey cards.

Hence, P(white) = P(grey) = $\frac{6}{12} = \frac{1}{2}$

(a)

The probability that number 9 card drawn is $\frac{1}{12}$

(b)

The probability that number 9 card drawn, given that the drawn card is white is,

P( 9 given white card) =$\frac{1/12 }{6/12}= \frac{1}{6}$