Question

1. Two golf balls are selected with replacement from a bowl containing 7 red and 3 blue balls
   1. What is the probability that both balls are red?
   2. What is the probability that both balls are blue?
   3. What is the probability that the first ball is red and the second ball is blue?
   4. What is the probability that the first ball is blue and the second ball is red?
   5. What is the probability that the two balls selected are the same color?
2. Adam goes to the grocery store. Suppose probability he buys milk is 40%, and the probability he buys steak is 70%, and the probability of both is 30%. What is the probability that he buys either milk or steak?
3. A car dealer has had issues with new cars that are being delivered with flawed paint and tires that are one too small. The two assembly shops are not related to one another. If the probability of flawed paint is 5% and the probability of the wrong size tire is 8%, then what is the probability that the next car delivered will have flawed paint and too small tires?

Answer 1

(1)

With replacement:

(a)

Selection 1: Red ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 1: Red ball) = 7/10 = 0.7

Selection 2: Red ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 2: Red ball) = 7/10 = 0.7

So,
P(Both balls are Red) = 0.7 X 0.7 = 0.49

So,

Answer is:

0.49

(b)

Selection 1: Blue ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 1: Blue ball) = 3/10 = 0.3

Selection 2: Blue ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 2: Blue ball) = 3/10 = 0.3

So,
P(Both balls are Blue) = 0.3 X 0.3 = 0.09

So,

Answer is:

0.09

(c)

Selection 1: Red ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 1: Red ball) = 7/10 = 0.7

Selection 2: Blue ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 2: Blue ball) = 3/10 = 0.3

So,
P(First ball Red & Second ball Blue) = 0.7 X 0.3 = 0.21

So,

Answer is:

0.21

(d)

Selection 1: Blue ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 1: Blue ball) = 3/10 = 0.3

Selection 2: Red ball

Red ball = 7

Blue ball = 3

Total balls = 10

So,

P(Selection 2: Red ball) = 7/10 = 0.7

So,
P(Selection 1 Blue & Selection 2: Red) = 0.3 X 0.7 = 0.21

So,

Answer is:

0.21

(e)

P(Both same color) = P(Both Red) + P(Both Blue)

                            = 0.49 + 0.09 = 0.58

So,

Answer is:

0.58

(2)

P(Milk) = 0.40

P(Steak) = 0.70

P(Milk & Steak)= 0.30

By Addition Theorem:
P(Milk OR Steak) = P(Milk) + P(Steak) - P(Milk & Steak)

                             = 0.40 + 0.70 - 0.30

                            = 0.80

So,

Answer is:

0.80

(3)

P(Flawed paint) = 0.05

P(Wrong size) = 0.08

By Multiplication Theorem:
P(Flawed paint AND Wrong size)= 0.05 X 0.08 = 0.0040

So,

Answer is:

0.0040