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:

Question

Question 5 options:

P(No more than 3 Tails)

P(Exactly 1 Tail)

P(At least 5 Tails)

P(Less than or equal to 2 Tails)

P(At least 1 Tail)

The standard deviation of the number of Tails

The mean number of Tails

P(Exactly 4 Tails)

P(No Tails)

P(More than 3 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

Binomial distribution,
n=10
p=0.28
q=1-0.28=0.72
mean=np
variance=npq
std dev=sqrt(npq)

Exactly r successes
=P(r)
=nCr p^r q^(n-r)

Work out each of the above problems and you will find a match.

For example, the first one:
P(no more than 3 tails)
=P(0)+P(1)+P(2)+P(3)
=0.037+0.146+0.255+0.264
=0.7021 (choice #2)
etc.

Post your answers for an answer check.

Answer 2

0.9626

Answer 3

2
5
7
1
3
9
10
8
6
4