1
Required:
a. What is the probability a player who buys one ticket will win the $2,500,000 prize?
b. What is the probability a player who buys one ticket will win the $10,000 prize?

1 Answer

2

Answer:

Step-by-step explanation:

From the given information;

The total number of ways to choose 7 number = ^{40}C_7

Number of ways to choose 7 correct numbers = ^{7}C_7

The probability P( win $2500000) is;

= \dfrac{^{7}C_7}{^{40}C_7}

= \dfrac{\dfrac{7!}{7!(7-7)!} }{\dfrac{40!}{7!(40-7)!}}

= \dfrac{1 }{\dfrac{40!}{7!(40-7)!}}

= \dfrac{1 }{\dfrac{40!}{7!(33)!}}

= \dfrac{1 }{18643560}

= 5.36 × 10⁻⁸

The probability P( win $10000) is:

= \dfrac{^7C_5 \times ^{33} C_2}{^{40}C_7}

= \dfrac{ \dfrac{7!}{5!(7-5)!} \times  \dfrac{33!}{2!(33-2)!} }{ \dfrac{40!}{7!(40-7)!}}

= \dfrac{ \dfrac{7!}{5!(2)!} \times  \dfrac{33!}{2!(31)!} }{ \dfrac{40!}{7!(33)!}}

= \dfrac{ 21 \times 528 }{ 18643560}

= \dfrac{ 11088 }{ 18643560}

=\dfrac{462}{776815}

= 5.95 × 10⁻⁴

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avatar
Reid Hamill
15.5k 3 10 26
answered 6 months ago