The probabilty that you will win at the lottery is 0.8. If you play the lottery 12 times, what is the probabilty that you will win at least 7 times?

Question

Not sure of the formula and if I did this problem right?

 

Can someone show the steps?

 

The probability that you will win at the lottery is 0.8. If you play the lottery 12 times, what is the probabilty that you will win at least 7 times?

 

Thanks

Answer 1

This problem belongs to the binomial distribution category.

 

You are interested in the probability that you win at least 7 times out of 12 trials knowing that the probability of success on each attempt is 0.80.

 

X ~ Bin(n=12, p = 0.80)

 

and we are looking for P[X≥7], i.e. P[X=7,8,9,10,11, or 12].

 

Either you use the Table for binomial probability or you have access to some sophisticated calculator or Excel.

In Excel you are looking for 

 

1- BINOMDIST(6,12,0.8, TRUE) = 0.9806.

 

 

You can also use "brute force" and compute

P[X=7] = ₁₂C₇ (0.8)⁷(0.2)⁵ = 0.0532

P[X=8] = ₁₂C₈(0.8)⁸(0.2)⁴ =  0.1329

etc...

P[X=12] = ....

 

and then you sum these numbers.