Mathematics, 30.07.2021 03:40 aesthvx44

An urn contains 5 blue marbles and 4 yellow marbles. One marble is removed, its color noted, and not replaced. A second marble is removed and its color is noted. (a) What is the probability that both marbles are blue? yellow?
(b) What is the probability that exactly one marble is blue?

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Answer from: edjiejwi

(a)The probability that both marbles are blue=5/18

The probability that both marbles are yellow=1/6

(b)The probability that exactly one marble is blue=5/9

Step-by-step explanation:

Blue marbles=5

Yellow marbles=4

Total marbles=5+4=9

(a)

Probability of drawing first blue marble=5/9

Probability of drawing second blue marble without replacement=4/8

The probability that both marbles are blue

$=\frac{5}{9}\times \frac{4}{8}=\frac{5}{18}$

Probability of drawing first yellow marble=4/9

Probability of drawing second yellow marble without replacement=3/8

The probability that both marbles are yellow

$=\frac{4}{9}\times \frac{3}{8}=\frac{1}{6}$

(b)

The probability that exactly one marble is blue

=Probability of first blue marble (Probability of second yellow marble)+Probability of first yellow marble (Probability of second blue marble)

The probability that exactly one marble is blue

= $\frac{5}{9}\times \frac{4}{8}+\frac{4}{9}\times \frac{5}{8}$

= $\frac{5}{18}+\frac{5}{18}$

= $\frac{10}{18}=\frac{5}{9}$

Answer from: Quest

Im not that good with division but i think 5 is -6but dont quote me on thatim not the best in division but thats my answer

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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