On Friday, $277 million worth of tickets were sold and more than $400 million in

Question

On Friday, $277 million worth of tickets were sold and more than $400 million in tickets were expected to be sold Saturday, according to Gary Grief, the executive director of the Texas Lottery. The drawing was held at 10:59 p.m. ET Saturday. The odds of nailing it are around 1 in 292 million. ”

According to this report, let’s assume that a total of $677 million worth of tickets were sold on last Saturday, and $2 per ticket . Use normal approximation to calculate the probability of no Powerball winners. Is it a reasonable approximation?

Explanation / Answer

No it is not a reasonable distribution because it is a discrete probability having two outcomes- winning and losing.

Hence poisson distribution should be used.

So we find the probability of no power ball winners by poisson distribution

Formula is :     

Where m is mean and

e is the base of natural logarithm .

Number of tickets sold =   = 388.5 million

Chance of winning is 1 in 292 million

m =

=

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