Question

An instant lottery game gives you probability 0.10 of winning on any one play. Plays are independent of each other. You play 4 times.

a) If X is the number of times you win, contract the probability distribution of X.

b) What is the probability that you don't win at all?

c) What is the probability that you win at least once?

d) What is the expected value of X? What is the standard deviation of X?

Answer 1

Part a)

Probability Mass Function of X is

Probability distribution of X

X	P ( X )
0	0.6561
1	0.2916
2	0.0486
3	0.0036
4	0.0001

Part b)

Part c)

P ( X >= 1 ) = 1 - P ( X = 0 )

P ( X >= 1 ) = 1 - 0.6561

P ( X >= 1 ) = 0.3439

Part d)

E ( X ) = n * P = 4 * 0.1 = 0.4