Respuesta :
Answer:
The probability you end up wearing two blue socks is [tex]\frac{1}{11}[/tex].
Step-by-step explanation:
Consider the provided information.
In your sock drawer you have 4 blue, 5 gray, and 3 black socks.
Total number of socks are: 4+5+3=12
[tex]Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
Number of favorable outcomes are 4 and total number of outcomes are 12.
The probability of garbing first blue socks is:
[tex]P(B_1) = \frac{4}{12}=\frac{1}{3}[/tex]
The probability of garbing second blue socks is:
[tex]P(B_2) = \frac{3}{11}=\frac{3}{11}[/tex]
Number of favorable outcomes are 3 and total number of outcomes are 11.
Therefore, the required probability is:
[tex]P(B_1,B_2)=\frac{1}{3}\times\frac{3}{11}=\frac{1}{11}[/tex]
Hence, the probability you end up wearing two blue socks is [tex]\frac{1}{11}[/tex].
Answer:
The probability that you end up wearing two blue socks is [tex]\dfrac{1}{11}[/tex].
Step-by-step explanation:
Given information:
Number of blue socks = 4
Number of gray socks = 5
Number of black socks = 3
Total number of socks = 4+5+3 = 12
We need to find the probability that you end up wearing two blue socks.
Total outcomes = [tex]^{12}C_2=\dfrac{12!}{2!(12-2)!}=66[/tex]
Favorable outcomes = [tex]^{4}C_2=\dfrac{4!}{2!(4-2)!}=6[/tex]
Formula for probability,
[tex]Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]Probability=\dfrac{6}{66}[/tex]
[tex]Probability=\dfrac{1}{11}[/tex]
Therefore, the probability that you end up wearing two blue socks is [tex]\dfrac{1}{11}[/tex].
Note: The given options are incorrect.
