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
V125BC [204]
4 years ago
9

Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5,

3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?A. 3/140B. 1/28C. 3/56D. 3/35E. 7/40
Mathematics
1 answer:
sweet-ann [11.9K]4 years ago
6 0

Answer:

The correct option is E.

Step-by-step explanation:

It is given that Alice, Benjamin, and Carol each try independently to win a carnival game.

Let A, B and C represent the following events.

A = Alice win

B = Benjamin win

C = Carol win

P(A)=\frac{1}{5} and P(A')=1-P(A)=1-\frac{1}{5}=\frac{4}{5}

P(B)=\frac{3}{8} and P(B')=\frac{5}{8}

P(C)=\frac{2}{7} and P(C')=\frac{5}{7}

We need to find the probability that exactly two of the three players will win but one will lose.

Probability=P(A\cap B\cap C')+P(A\cap B'\cap C)+P(A'\cap B\cap C)

Probability=P(A)P(B)P(C')+P(A)P(B')P(C)+P(A')P(B)P(C)

Probability=\frac{1}{5}\cdot\frac{3}{8}\cdot\frac{5}{7}+\frac{1}{5}\cdot\frac{5}{8}\cdot\frac{2}{7}+\frac{4}{5}\cdot\frac{3}{8}\cdot\frac{2}{7}

Probability=\frac{3}{56}+\frac{1}{28}+\frac{3}{35}

Probability=\frac{7}{40}

The probability that exactly two of the three players will win but one will lose is \frac{7}{40}.

Therefore the correct option is E.

You might be interested in
What is 35% of 35? please included how you got it!!
ruslelena [56]

\huge\boxed{12.25}

First, convert the percentage to a decimal. You can do this by moving the decimal place two places to the left.

35\%\longrightarrow0.35

Now, simply multiply that decimal by 35 using a calculator.

0.35*35=\boxed{12.25}

4 0
4 years ago
Read 2 more answers
Please help asap :)
Kryger [21]

Answer:

a. 180 - 10 = 170

b. 360/10 = 36

3 0
3 years ago
Janice examines the given triangle and estimates that
den301095 [7]

Answer:

Janice examines the given triangle and estimates that the longest side has a length of 25 units―if it is a right triangle. How does her estimate compare to the actual length? It is under by approximately 0.6 units.

Step-by-step explanation:

4 0
3 years ago
The width of a rectangle is 1m less than half of its length, and the perimeter is 46m. Find the dimensions.
VLD [36.1K]
The width is 15.
The length is 31.
6 0
4 years ago
Use the diagram above and round your answer to the nearest hundredth. If a is 6 in. and angle a = 31º, what is b?
Romashka [77]
 <span>If angle B = 60, and angle C is a right angle, then angle A is 30 degrees 
tan 30 = b/c 
.577 = 10/c 
c = 17.32  ...</span>
4 0
3 years ago
Read 2 more answers
Other questions:
  • Antonio was playing a matching game where he had to pair up each inequality with the graph of its solution. Write the letter of
    13·1 answer
  • What is the factor of 4x + 10
    15·1 answer
  • Some students want to know if residents of their town are in favor of building a new school. Kevin surveys all of the residents
    7·1 answer
  • find the first six terms of the sequence. a1 = -6, an = 4 • an-1 select one: a. 0, 4, -24, -20, -16, -12 b. -24, -96, -384, -153
    14·1 answer
  • What is the prime factorization for 356
    10·1 answer
  • What is the shape of the two-dimensional cross section?
    8·1 answer
  • Consider the diagram and angle measurements shown below.
    11·2 answers
  • What does x equal? ​
    14·2 answers
  • PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU B
    5·2 answers
  • Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!