Question

Problem 6. (Binomial distribution) A company produces light bulbs. Each bulb is checked before it leaves the company. The trans port damages 5% of the bulbs though. Assume you have bought 10 bulbs a) What is the probability that no bulb is damaged? b) What is the probability that exactly one bulb is damaged? c) What is the probability that at most two bulbs are damaged? d) What is the probability that at least two bulbs are damaged? Problem 7. (Hypergeometric distribution) In a lottery seven balls are drawn out of 42 balls without replacement of the drawn balls Assume you have filled out a lottery batch (1) What is the probability that you chose all seven numbers cor- rectly? (2) What is the probability that you chose exactly four numbers correctly?

Answer 1

Ans:

6)

Binomial distribution with n=10 and p=0.05

P(x=k)=10C_k*0.05^k*(1-0.05)^10-k

x	p(x)
0	0.5987
1	0.3151
2	0.0746
3	0.0105
4	0.0010
5	0.0001
6	0.0000
7	0.0000
8	0.0000
9	0.0000
10	0.0000

a)P(x=0)=(1-0.05)¹⁰=0.5987

b)P(x=1)=10C₁*0.05¹*0.95⁹=0.3151

c)P(x<=2)=P(x=0)+P(x=1)+P(x=2)

=0.5987+0.3151+0.0746=0.9885

d)

P(x>=2)=1-P(x=0)-P(x=1)

=1-0.5987-0.3151=0.0861