Question

A drawer contains 7 white socks and 3 black socks. If three socks are selected simultaneously from the drawer, what is the probability that 1 is white and two are black?

Question 2
A committee of 3 people are selected from 3 juniors and 5 seniors. What is the probability the committee will contain at least two seniors?

Question 3
An experiment has 4 outcomes. Outcome 1 is three times outcome 3. Outcome 2 is equally likely to outcome 3. Outcome 4 is twice as likely as outcome 3. What is the probability outcome 1 will occur?

Answer 1

1.
\[required~probability=\frac{ C_{1}^{7}\times C_{2}^{3} }{ C _{3}^{10} }\]
\[P=\frac{ \frac{ 7 }{ 1 }\times \frac{ 3 \times 2 }{ 2 \times 1 } }{ \frac{ 10 \times 9 \times 8 }{ 3 \times 2 \times 1 } }\]
\[P=\frac{ 21 }{ 120}=\frac{ 7 }{ 40 }\]
2nd and 3rd solve similarly

Answer 2

Idk

Answer 3

x.x

Answer 4

2.
probability at least 2 seniors=probability no juniors and 3 seniors+probability 1 junior and 2 seniors
\[P= \frac{ C_{3}^{5} }{C _{3}^{8} } +\frac{ C _{1}^{3} \times C _{2}^{5} }{ C _{3}^{8} }\]
\[P=\frac{ \frac{ 5\times4\times3 }{ 3\times2\times1} }{ \frac{ 8\times7\times6 }{ 3\times2\times1 } }+\frac{ \frac{ 3 }{ 1} \times \frac{ 5\times4 }{ 2 \times1}}{ \frac{ 8\times7\times6}{ 3\times 2\times1 }}\]
\[P=\frac{ 10 }{ 56 }+\frac{ 30 }{ 56 }=\frac{ 40 }{ 56 }=\frac{ 5 }{ 7 }\]