Complete Question
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
Answer:
(a) The probability that all four balls are red is
0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
1.398
Step-by-step explanation:
An urn contains
Red balls = 8
White balls = 6
Green balls = 4
Total number of balls = 18 balls
(a) The probability that all four balls are red is?
The probability that a ball drawn is red = 8/18
The probability of drawing a ball that is not red = 1 - 8/18 = 10/18
The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15
= 1680/73440
= 0.022875817
Approximately = 0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls
RRGG
GGRR
RGRG
GRGR
RGGR
GRRG
P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)
=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways
= 672/73440 × 6 ways
= 0.0091503268 × 6 ways
= 0.0549019608
Probability of drawing out exactly two two red balls and two green balls is
= 0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)
P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)
=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways
=0.1830065359 + 0.05
= 0.2330065359 × 6 ways
= 1.3980392154
≈1.398
