# Quod Erat Demonstrandum

## 2010/12/23

### to 5D

Filed under: Additional / Applied Mathematics,NSS — johnmayhk @ 11:32 下午
Tags:

Solution to questions (2010-12-22 worksheet)

1.
Toss a fair coin 10 times.

P(exactly 6 “H” and 4 “T”)

= $C^{10}_4(\frac{1}{2})^4(\frac{1}{2})^6$ (or $\frac{C^{10}_4}{2^{10}}$)

2.
There are 100 tickets, 3 out of them are “lucky” ticket. 5 boys are randomly given the 100 tickets, each of them gets 1 ticket.

P(exactly 2 boys get “lucky” tickets)

= $\frac{C^3_2C^{97}_3}{C^{100}_5}$

3.
A sub-committee of 6 members is selected at random from the 15 members of a committee, 10 of whom are women and 5 men.

P(the sub-committee includes at least 2 men)

= $1 - \frac{C^{10}_6 + C^{10}_5C^5_1}{C^{15}_6}$

4.
There are 9 couples in a room. If 6 people are chosen at random,

P(exactly 2 couples selected)

= $\frac{C^9_2C^7_2(2^2)}{C^{18}_6}$