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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.

Respuesta :

Answer:

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.

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