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
Write the inequality given in the diagram below
11111nata11111 [884]

Answer:

x ≥ - 1

Step-by-step explanation:

the solid circle above - 1 on the number line indicates that x can equal - 1

the arrow points right indicating x is greater than or equal to - 1 , that is

x ≥ - 1

4 0
1 year ago
Find the diameter of a dinner plate whose circumference is about 19 inches
vodka [1.7K]
The answer is 4.6
                               the equation is 19 * 4.13
8 0
3 years ago
What is 3/4-5/10 in simplest form
Nezavi [6.7K]
3/4 is as simple as it gets 5/10- 1/2
5 0
3 years ago
if caramel is put onto a sphere-shaped apple such that the surface area increase at a rate of 10 cm2/min, find the rate at which
tresset_1 [31]

Answer:

The diameter will increase at a rate of 1/30π cm/min

Step-by-step explanation:

Here we want to calculate the rate at which the diameter will increase

Mathematically, the area of a sphere is given as;

A = 4πr^2

But r = d/2

so A = 4 * π * d/2 * d/2 = πd^2

dA/d(d) = 2πd

Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π

Given dA/dt = 10

Mathematically;

d(d)/dt = d(d)/dA * dA/dt

dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min

5 0
3 years ago
Select the correct word form for 87,055​
sveticcg [70]

Answer: Eighty-seven thousand-fifty five

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Correct answer gets brainliest.
    5·2 answers
  • Explain how using basic facts can help you find 10x20x30x40 mentally
    8·2 answers
  • How to solve the equation 2(8 + k) =22 by using the properties of equality ? <br> Please Answer
    6·2 answers
  • Identify the domain and range of the function graphed below.
    13·1 answer
  • What’s the answer to this question?
    9·1 answer
  • Is <img src="https://tex.z-dn.net/?f=2%5E%7B-3%7D" id="TexFormula1" title="2^{-3}" alt="2^{-3}" align="absmiddle" class="latex-f
    14·1 answer
  • This question so hard pls helps
    9·1 answer
  • Part A: What is the shortest distance between the gymnasium and the library? Round your answer to the nearest tenth of a kilomet
    12·1 answer
  • DO NOW: What is the surface area of the cube? 4 in 4 in 4 in​
    10·1 answer
  • Can you help please help
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!