A special deck of 16 card has 4 that are blue 4 yellow 4 gre

A special deck of 16 card has 4 that are blue, 4 yellow, 4 green and 4 red. The four cards of each color are numbered from one to four. A single is drawn at random. Find the following probabilities.

a. The probability that the card drawn is a two or a four.

b. The probability that the card is a two or a four, a given that is not a one.

c. The probability that the card is a two or four, given that it is either a two or a three.

d The probability that the card is a two or a four, given that it is red or green.

A random experiment gave rise to the two way contingency table shown. Use it to compute the probabilities indicated.

R

S

A

0.12

0.18

B

0.28

0.42

b. Based on the answer to (a). determine whether or not the events A and R are independent.

c. Based on the answer to (b). determine whether or not P(A|R) can be predicted without any computation. If so, make the prediction. In any case, compute P(A|R) using the rule for conditional probability.

A random experiment gave rise to the two way contingency table shown. Use it to compute the probabilities

R

S

A

0.13

0.07

B

0.61

0.19

b. Based on the answer to (a). determine whether or not the events A and R are independent.

c. Based on the answer to (b). determine whether or not P(A|R) can be predicted without any computation. If so, make the prediction. In any case, compute P(A|R) using the rule for conditional probability.

Solution