Binomial Distribution Questions
1. Sue throws a fair coin 15 times and records the number of times it shows a head.
(a) State the distribution to model the number of times the coin shows a head. (2)
Find the probability that Sue records
(b) exactly 8 heads, (2)
(c) at least 4 heads. (2)
2. A disease occurs in 3% of a population.
(a) State any assumptions that are required to model the number of people with the disease in a random
sample of size n as a binomial distribution.
(2)
(b) Using this model, find the probability of exactly 2 people having the disease in a random sample of
10 people.
(3)
(c) Find the mean and variance of the number of people with the disease in a random sample of 100
people.
(2)
3. A fair coin is tossed 4 times.
Find the probability that
(a) an equal number of head and tails occur (2)
(b) all the outcomes are the same, (3)
(c) the first tail occurs on the third throw. (2)
4. An unfair coin with probability of heads
p
is tossed 20 times. The probability of seeing no heads is 0.1.
Determine
p
(3)
5. I play a game for which the probability of winning is
0.7
. If I win every game, what is the smallest
number of times I play such that the probability of winning every game is less than 0.01? (3)
6. Given that:
a.
X B
(10
,
0.2)
, determine the smallest
k
such that
P
(
X ≥ k
)
≤
0.1
(3)
b.
X B
(15
,
0.75)
, determine the largest
k
such that
P
(
X
<
k
)
≥
0.8
(5)
Total Marks: 34. Bronze: 24, Silver: 27, Gold: 31, Platinum: 34
