Question

A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes
1. Contain no heads?
2. Contain exactly three heads?
3. Contain at least three heads?
4. Contain more heads than tails?

Answer 1

Answer:

a) Each flip can be either heads or tails, so there are 210 = 1024 possible outcomes. b) To specify an outcome that has exactly two heads, we simply need to choose the two flips that came up heads. There are C(lO, 2) = 45 such outcomes

Answer 2

Answer:

(a ) are there in total ?

2^10 = 1024

B) contain exactly two heads?

C(10,2)= (10!/(2!*8!))

The answer is 45.

C)contain at most three tails?

C(10,3)+C(10,2)+C(10,1)+C(10,0)

=((10!/(3!*7!)) + (10!/(2!*8!)) + (10!/(1!*9!)) + (10!/(0!*10!))

= 120 + 45 + 10 + 1

The answer is 176.

D)contain the same number of heads and tails?

5 head,5tail(exactly5 head,exactly 5 tail)

= (10!/(5!*5!))

The answer is 252.