Answer: $4.11
Step-by-step explanation:
Given: To win the jackpot in Massachusetts, we have to correctly guess all six numbers drawn from a pool of 36.
The number of combinations of 6 numbers drawn from a pool of 36 is given by :-
[tex]^{36}C_6=\dfrac{36!}{6!(36-6)!}\\\\=\dfrac{36\times35\times34\times33\times32\times31\times30!}{6!30!}\\\\=1947792[/tex]
Now, the probability of winning the prize = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]p=\dfrac{1}{1947792}[/tex]
Now, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = [tex]p\times\text{Amount}[/tex]
[tex]\dfrac{1}{1947792}\times8000000=4.1072147334\approx\$4.11[/tex]
Hence, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = $4.11
