Question

Suppose 5% of cereal boxes contain a prize. You are determined to buy cereal boxes until you win a prize.

A) What kind of probability distribution is this, and explain your choice.

B) What is the probability that you win a prize on the 2nd box?

C) Find the mean and standard deviation of this distribution

Answer 1

X: number of cereal boxes purchased until you win a prize.

a). we will use GEOMETRIC distribution.

[ here the number of trials are unknown .Also,  the trials are independent and the probability of success (p) is fixed.so, we can conclude that X ~ geometric (0.05 ).

the pmf of the distribution is :-

$P(X=x)=(1-0.05)^{x-1}*0.05$]

b). the probability that you win a prize on the 2nd box is:-

$P(X=2)=(1-0.05)^{2-1}*0.05=\mathbf{0.0475}$

c).the mean of this distribution is :-

20 р 0.05

standard deviation of the distribution is :-

$=\sqrt{\frac{1-p}{p^2}}=\sqrt{\frac{1-0.05}{0.05^2}}\approx\mathbf{19.49}$

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