17. An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) Compute P(all four are red).
(b) Compute P(exactly two are red and exactly two are green).
(c) Compute P(exactly two are red or exactly two are green).
(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
(Type an integer or a decimal. Round to two decimal places as needed.)

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

(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

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step-by-step explanation:

the answer is 13 cm