Answer :
Answer:
The required probability is [tex]\frac{1}{231}[/tex].
Step-by-step explanation:
Probability:
The ratio of the number of favorable outcomes to the number of possible outcomes.
Multiplication Rule:
P(A and B)= P(A ∩ B)= P(A)×P(B|A) =P(B)×P(A|B)
Addition Rule for disjoint events :
P(A or B) =P(A∪B)=P(A)+P(B)
Given, 10 white socks (W), 6 black socks (B), 4 red socks (R) and 2 purple socks (P).
Total number of socks =(10+6+4+2)=22
Probability of getting a purple sock on first drawn
=P(P₁)
[tex]=\frac{\textrm{The number of purple socks}}{\textrm{Total number of socks}}[/tex]
[tex]=\frac{2}{22}[/tex]
[tex]=\frac{1}{11}[/tex]
After one purple socks is drawn,
The number of purple socks is =(2-1) =1
Total number of socks= (22-1)=21
Probability of getting a purple sock on second drawn
=P(P₂|P₁)
[tex]=\frac{\textrm{The number of purple socks}}{\textrm{Total number of socks}}[/tex]
[tex]=\frac{1}{21}[/tex]
The probability of polling matching pair of purple socks is
=P(P₁)×P(P₂|P₁)
[tex]=\frac{1}{11}\times \frac{1}{21}[/tex]
[tex]=\frac{1}{231}[/tex]