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1. It is known that a computer part produced by a certain machine will be defective with probability 0.1, and parts are produced independently of each other. What is the probability that in a sample of 10 items at most one will be defective?

Let X = number of defectives in a sample of 10. Then X

∼

Bin (10 , .

1)

P ( X = 0) + P ( X = 1) =

10

( .

1)

0

( .

9)

10

+

10

( .

1)

1

( .

9)

9

0 1

= 1

×

1

×

.

3486784 + 10

×

.

1

×

.

38742

= .

7361

2. An exciting computer game is released. Sixty percent of players complete all levels.

Thirty percent of them will then buy an advanced version of the game. Among 15 users, what is the expected number of people who will buy the advanced version?

What is the probabilty that at least two people will buy it?

Let X be the number of people who will buy the advanced version (“buy advanced version”=Success!)

To use the Binomial model, need p = P (buy advanced version) p =

=

P (buy advanced version)

P (buy advanced version

| complete all levels) P (complete all levels)

= ( .

03)( .

6) = .

18

Thus we have X

∼

Bin (15 , .

18) and therefore

E [ X ] = np = 15( .

18) = 2 .

7 and

P ( X

≥

2) = 1

−

P ( X = 0)

−

P ( X = 1) = 1

−

(1

− p ) n

− np (1

− p ) n

−

1

= 0 .

7813

1