Question

There are 9 black balls and 5 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer #1

Black balls = 9

Red balls = 5

Total balls = 14

Number of balls drawn = 4

Case 1: 3 Black balls & 1 Red ball drawn

Number of ways of drawing 4 balls from 14 balls is:

Number of ways of drawing 3 Back balls from 9 back balls is

Number of ways of drawing 1 Red ball from 5 Red balls is:

So,

P(3 Black balls) = 84 X 5/ 1001 = 0.4196

Case 2: 4 Black balls drawn

Number of ways of drawing 4 balls from 14 balls is:

Number of ways of drawing 4 Back balls from 9 back balls is

So,

P(4 Black balls) = 126/ 1001 = 0.1259

So,

P(At least 3 Black balls) = 0.4196 + 0.1259 = 0.5455

So,

Answer is:

**0.5455**

There are 6 black balls and 5 red balls in an urn. If 4 balls
are drawn without replacement, what is the probability that exactly
2 black balls are drawn? Express your answer as a fraction or a
decimal number rounded to four decimal places.

There are 5 black balls and 10 red balls in an urn. If 3 balls
are drawn without replacement, what is the probability that no
black balls are drawn? Express your answer as a fraction or a
decimal number rounded to four decimal places.

There are 8 black balls and 7 red balls in an urn. If 4 balls
are drawn without replacement, what is the probability that no more
than 1 black ball is drawn? Express your answer as a fraction or a
decimal number rounded to four decimal places.

Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 4 red balls and 2
black balls. If an urn is selected at random and a ball is
drawn, find the probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.
P(red)=

Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 4
red balls and 1 black ball. Urn 3 contains 4 red balls and 3 black
balls. If an urn is selected at random and a ball is drawn, find
the probability that it will be red.
enter your answer as a decimal rounded to 3 decimal places

Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 3 red balls and 1 black
ball. If an urn is selected at random and a ball is drawn, find the
probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.

An urn contains 5 red and 9 pink balls. Four balls are randomly
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the urn. What is the probability that all 4 balls drawn from the
urn are red? Round your answer to three decimal places.

An urn contains 4 red balls and 6 green balls. Three balls are
chosen randomly from the urn, without replacement. (a) What is the
probability that all three balls are red? (Round your answer to
four decimal places.) (b) Suppose that you win $50 for each red
ball drawn and you lose $25 for each green ball drawn. Compute the
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Refer to Example 4.40. An urn contains eight red balls, eight
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drawn at random without replacement.
Compute the probability that the sample contains at least one ball
of each color. (Round your answer to four decimal places.)

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balls?
2.cards are drawn at random from an ordinary deck of 52,one by
one without replacement.what is the probability that no king is
drawn before the ace of spades is drawn?

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