Answer:
a) 0.1429
b) 0.2667
c) 0.3067
d) 0.3524
Step-by-step explanation:
Blue = 6
Gray = 7
Black = 2
Number of socks = 15
a) 2 blue socks.
The probability of getting two consecutive blue socks is:
[tex]P(Blue=2) = \frac{6}{15}*\frac{5}{14}=0.1429[/tex]
b) no gray socks.
The probability of getting no grey socks with two picks is:
[tex]P(G=0) = \frac{15-7}{15} *\frac{14-7}{14}=0.2667[/tex]
c) at least 1 black sock.
The probability of getting at least one black sock is:
[tex]P(B>0) = 1 - P(B=0)\\P(B>0) =1 - (\frac{13}{15}*\frac{12}{15})\\P(B>0) = 0.3067[/tex]
d) matching socks.
The probability of getting matching socks is the sum of the probabilities of getting 2 black, 2 blue or 2 gray socks:
[tex]P(matching) = P(Blue=2)+P(Black=2)+P(G)\\P(matching) =\frac{6}{15}* \frac{5}{14} +\frac{2}{15}* \frac{1}{14}+\frac{7}{15}* \frac{6}{14} \\P(matching) = 0.3524[/tex]
