1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
abruzzese [7]
2 years ago
12

In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and 7 of them are drawn at random. If the 7

numbers drawn match the 7 numbers a player has chosen, in any order, she or he win $2,500,000. Alternatively, if 6 of the numbers drawn match 6 of the 7 numbers a player has chosen, in any order, the player wins $40,000, and if 5 of the numbers drawn match 5 of the 7 numbers a player has chosen, in any order, the player wins $10,000.
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?
Mathematics
1 answer:
DENIUS [597]2 years ago
8 0

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

You might be interested in
Which of the following is equal to the rational expression when x -2 or -6?
kykrilka [37]

The given expression is

f(x) = \frac{3(x+2}{(x+2)(x+6)}

And since we have x+2 common in numerator and denominator, there is a hole at x+2=0, that is at x=-2

And a function is undefined when denominator is zero. And at x=-6, denominator become zero.

So, at x=-6, the function is undefined, or there is a vertical asymptote at x=-6 and hole at x=-2 .

4 0
3 years ago
These can come from many different places including national, state, public, and private sources. This money can be awarded base
Serhud [2]

Answer:

D. Grants

Step-by-step explanation:

Although grants and scholarships are similar, grants tend to be for financial reasons, therefore it would be grant. Hope this helped :)

5 0
3 years ago
Read 2 more answers
What is 2x+7y=28 in slope intercept form
Artyom0805 [142]

Answer:

y = -2/7x + 4

4 0
3 years ago
Factor completely 2x^3y^4-8x^2y^3+6xy^2
Maru [420]

Answer:

2 x y^2 (x y - 1) (x y - 3)

Step-by-step explanation:

2x^3y^4-8x^2y^3+6xy^2

each term contains 2xy^2 so factor that out

2xy^2(x^2y^2 -4xy+3)

then lets factor the inside

what terms multiply together to give us +3 and add to -4

-3* -1 = 3     -3+-1 =-4

2 x y^2 (x y - 1) (x y - 3)

6 0
3 years ago
What is 560 miles in 10hours ?
Gala2k [10]

A good way to think about this is take the phrase "miles in hours" from the question. You are given "560 miles in 10 hours" and what you need to figure out is "X miles in 1 hours." To go from 10 hours to 1 hour, you divide by 10. So you also want to divide miles by 10 to keep everything consistent. 560/10 = 56 miles.

<h3>The answer is 56 miles.</h3>
7 0
2 years ago
Other questions:
  • An object is launched upward
    7·1 answer
  • Factor each expression and explain how you solved it.
    9·1 answer
  • Rectangle 30 ft wide and 70 feet long. How long would diagonal corners be?
    14·1 answer
  • What is the Einstein theory
    11·1 answer
  • 10x+9=4x -9 solve <br><br> please help
    12·1 answer
  • HELP ASAP WILL GIVE BRAINLIEST!! Write the equation in point-slope form for the line that contains the points
    12·1 answer
  • 2.
    14·1 answer
  • What is 12x1,234+55 divided by 6
    8·2 answers
  • The sum of three numbers is 20. The sum of twice the first number, 5 times the second
    9·1 answer
  • A quadratic function has zeros at 1 and -8. Which of the following could be the function?​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!