## 8.7 Coin And Die Problem

### 8.7.1 Tossing A Coing Twice

First Coin
H T
Second
Coin
H HH HT
T TH TT

Tossing a coin twice is equivalent to tossing two coins at once

What is the probability that

1. The Head appears at the first draw?
2. At least one Head appears?
3. Less than two Heads appear?
4. Only Tails appears?

### 8.7.2 Flipping A Coin Thrice

First Two Flips
HH HT TH TT
Third Flip H HHH HHT HTH HTT
T THH THT TTH TTT

What is the probability that

1. All three are Heads?
2. There are more than one Head?
3. The second draw gives a Head?
4. The third draw does not give a head?
5. The first draw gives a Tail but the the Draw does not?
6. At most one Head appears?

### 8.7.3 Flinging Two Dice at Once

Tossing Two
Dice at Once
First Die
1 2 3 4 5 6
Second
Die
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6

What is the probability that

1. The first numbers is odd?
2. The summation of numbers in two draws is a prime number?
3. Both numbers are same?
4. The second number is bigger?