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. 1/2 or 0.5

b. 2/3 or 0.67

c. 1/2 or 0.5

d. 1/2 or 0.5

Step-by-step explanation:

a) P (2 or 4) = ?

P (2 or 4) = P (2) + P (4)

1={b1, y1, g1, r1}

2={b2, y2, g2, r2}

3={b3, y3, g3, r3}

4={b4, y4, g4, r4}

P (2 or 4) = ?

2 or 4={b2, y2, g2, r2} or {b4, y4, g4, r4}

2 or 4={b2, b4, y2, y4, g2, g4, r2, r4}

P (2 or 4) = 8/16=1/2

Thus, the probability that the card drawn is a two or a four is 0.5.

b) P (2 or 4 / not one) = ?

P (2 or 4 / not one) = P (2 or 4 and not one) / P (not one)

not 1={b2, y2, g2, r2, b3, y3, g3, r3, b4, y4, g4, r4}

P (not one) = 12/16=3/4

2 or 4 and not one={b2, b4, y2, y4, g2, g4, r2, r4} and {b2, b3, b4, y2, y3, y4, g2, g3, g4, r2, r3, r4} = {b2, b4, y2, y4, g2, g4, r2, r4}

P (2 or 4 and not one) = 8/16=1/2

P (2 or 4 / not one) = 1/2/3/4=4/6=2/3

Thus, the probability that the card is a two or a four, a given that is not a one is 0.67

c) P (2 or 4 / 2 or 3)

P (2 or 4 / 2 or 3) = P (2 or 4 and 2 or 3) / P (2 or 3)

P (2 or 3) = ?

2 or 3={b2, y2, g2, r2} or {b3, y3, g3, r3}

2 or 3={b2, b3, y2, y3, g2, g3, r2, r3}

P (2 or 3) = 8/16=1/2

2 or 4 and 2 or 3={b2, b4, y2, y4, g2, g4, r2, r4} and {b2, b3, y2, y3, g2, g3, r2, r3}

2 or 4 and 2 or 3={b2, y2, g2, r2}

P (2 or 4 and 2 or 3) = 4/16=1/4

P (2 or 4 / 2 or 3) = (1/4) / (1/2) = 2/4=1/2

Thus, the probability that the card is a two or four, given that it is either a two or a three is 0.5.

d) P (2 or 4 / red or green)

P (2 or 4 / red or green) = P (2 or 4 and red or green) / P (red or green)

red or green={r1, r2, r3, r4} or {g1, g2, g3, g4}

red or green={r1, r2, r3, r4, g1, g2, g3, g4}

P (red or green) = 8/16=1/2

2 or 4 and red or green={b2, b4, y2, y4, g2, g4, r2, r4} and {r1, r2, r3, r4, g1, g2, g3, g4} = {r2, r4, g2, g4}

P (2 or 4 and red or green) = 4/16=1/4

P (2 or 4 / red or green) = (1/4) / (1/2) = 2/4=1/2

Thus, the probability that the card is a two or a four, given that it is red or green is 0.5.