Question

Suppose Tori has an unfair coin which lands on Tails with probability 0.28 when flipped. If she flips the coin 10 times, find each of the following:

	The mean number of Tails
	P(Less than or equal to 2 Tails)
	P(No more than 3 Tails)
	P(No Tails)
	P(At least 1 Tail)
	P(Exactly 1 Tail)
	P(Exactly 4 Tails)
	P(At least 5 Tails)
	P(More than 3 Tails)
	The standard deviation of the number of Tails

1.	0.1798
2.	0.7021
3.	2.8
4.	0.1181
5.	0.1456
6.	0.0374
7.	0.9626
8.	0.2979
9.	0.4378
10.	1.42

Answer 1

Ans:

Given that

n=10 and p=0.28

Mean=np=10*0.28=2.8

standardd deviation=sqrt(np*(1-p))=sqrt(10*0.28*0.72)=1.42

P(x=k)=10C_k*0.28^k*(1-0.28)^10-k

x	p(x)
0	0.0374
1	0.1456
2	0.2548
3	0.2642
4	0.1798
5	0.0839
6	0.0272
7	0.0060
8	0.0009
9	0.0001
10	0.0000

The mean number of tails	2.8
P(Less than or equal to 2 Tails)	0.4378
P(No more than 3 Tails)	0.7021
P(No Tails)	0.0374
P(At least 1 Tail)	0.9626
P(Exactly 1 Tail)	0.1456
P(Exactly 4 Tails)	0.1798
P(At least 5 Tails)	0.1181
P(More than 3 Tails)	0.2979
The standard deviation of the number of Tails	1.42