Question

One drawer in a dresser contains 8 blue socks and 6 white socks. a second drawer contains 4 blue socks and 2 white socks. one sock is chosen from each drawer. what is the probability that they match (same color)?

Answer 1

The probability of drawing a blue sock from the first drawer is 8/14 = 4/7.
The probability of drawing a white sock from the first drawer is 6/14 = 3/7.
The probability of drawing a blue sock from the second drawer is 4/6 = 2/3.
The probability of drawing a white sock from the second drawer is 2/6 = 1/3.
$P(blue\ blue) = \frac{4}{7}\times\frac{2}{3}=\frac{8}{21}$
$P(white\ white)=\frac{3}{7}\times\frac{1}{3}=\frac{3}{21}$
The probability that they match is therefore (8/21) + (3/21) = 11/21
The answer is 11/21.

Answer 2

The probability that they match (same color) is 11/21.

What is probability?

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

First drawer contains 8 blue socks and 6 white socks.

Total number of socks in first drawer = 14

Second drawer contains 4 blue socks and 2 white socks.

Total number of socks in second drawer = 6

Choosing one socks from each drawer,

P(Blue) = $\frac{8}{14}$ × $\frac{4}{6}$

⇒ $\frac{8}{21}$

P(white) = $\frac{6}{14}$ × $\frac{2}{6}$

⇒ $\frac{1}{7}$

The probability that they match,

$P(e)=\frac{8}{21}+\frac{1}{7}$

⇒ $\frac{8+3}{21}$

⇒ $\frac{11}{21}$

Hence we can conclude that the probability that they match (same color) is 11/21.

Learn more about probability here

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