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
Marrrta [24]
3 years ago
15

A track star runs two races on a certain day. The probability thathe wins the first race is 0.7, the probability that he wins th

esecond race is 0.6, and the probability that he wins both races is0.5. Find the probability that:
A) he wins at lease one race.
B) he wins exactly one race.
C) he wins neither race
Mathematics
1 answer:
NARA [144]3 years ago
6 0

Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

A = a + (A \cap B)

In which a is the probability that he wins the first race but not the second and A \cap B is the probability that he wins both these races.

By the same logic, we have that:

B = b + (A \cap B)

The probability that he wins both races is 0.5.

This means that A \cap B = 0.5

The probability that he wins the second race is 0.6

This means that B = 0.6

B = b + (A \cap B)

0.6 = b + 0.5

b = 0.1

The probability that he wins the first race is 0.7.

This means that A = 0.6

A = a + (A \cap B)

0.7 = a + 0.5

a = 0.2

A) he wins at least one race.

This is

P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

P = a + b = 0.2 + 0.1 = 0.3

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

You might be interested in
Haylie and Justin went camping with their families for 7 days. They each took their own bottles of water. Haylie drank 6 bottles
trasher [3.6K]

Haylie took 48 bottles of water on the trip.

4 0
3 years ago
The table shows the number of feathers Patsy the Peacock sold at each of the 8 festivals this year.
Vlada [557]

Answer:

75%

Step-by-step explanation:

It's right

6 0
3 years ago
Read 2 more answers
The graph of g(x) is the result of translating the graph of f(x) = 3* six units to the right. What is the equation
Doss [256]

Answer:

Step-by-step explanation:

Pls help me with my question roo

3 0
3 years ago
A test has 10 true/false questions. How many different tests can be turned in to the teacher?
Flauer [41]
The same as the greatest number that can be written
with 10 binary bits:  <u>1,024</u>
3 0
3 years ago
Read 2 more answers
How do you get the measure of center?
Irina18 [472]
To get the center of the measurement, you. could use a ruler.
8 0
3 years ago
Other questions:
  • PLEASE HELP !!!!!!!
    6·2 answers
  • Write and solve an equation.
    6·2 answers
  • How do you calculate the area of a trapezoid?
    8·1 answer
  • Simply expression 12x-3x
    10·2 answers
  • In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as
    14·1 answer
  • How to do this math exercise 4x-2y=60<br> 4x-3y=26
    14·2 answers
  • Henri conducts an experiment to determine who likes peanut butter more: boys or girls. He has 25 girls and 25 boys taste some pe
    15·1 answer
  • (3•x)•3-2=1 <br><br> I missed a lot of school and don’t know how to solve for x could you help me
    7·1 answer
  • 7​% of ​$582 is how​ much?
    8·2 answers
  • It took Madge 45 minutes to get to school after she woke up. If she arrived at school at 8:35, what time did she wake up?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!