Answered

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There are 18 black and 12 navy socks in your drawer. The room is dark and you
cannot turn on the light. What is the least number of socks that you have to take out of
your drawer to be certain that you have a pair of black socks?

There Are 18 Black And 12 Navy Socks In Your Drawer The Room Is Dark And You Cannot Turn On The Light What Is The Least Number Of Socks That You Have To Take Ou class=

Sagot :

The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.

Given that,

There are 18 black socks and 12 Navy socks in your drawer the room is dark and you cannot turn on the light.

We have to determine

What is the least number of socks that you have to take out of  your drawer to be certain that you have a pair of black socks?

According to the question,

The following steps can be used in order to determine the least number of socks that you have to take out of the drawer:

The total number of blue socks is 18,

And the total number of navy socks is 12.

The probability that the socks come out is black socks is,

[tex]\rm P_b = \dfrac{18}{18+12}\\\\P_b= \dfrac{18}{30}\\\\P_b = \dfrac{3}{5}[/tex]

And the probability that the socks come out is navy socks is,

[tex]\rm P_n = \dfrac{12}{18+12}\\\\P_n= \dfrac{12}{30}\\\\P_n = \dfrac{2}{5}[/tex]

On comparing both the probability,

[tex]\rm P_b>P_n[/tex]

Hence, The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.

For more details refer to the link given below.

https://brainly.com/question/19200823

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