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
alina1380 [7]
3 years ago
12

Benny is trying to learn how to ride a bike, but is terrified of falling. He did some research, and discovered that if he rides

a bike with training wheels, the probability of falling is 0.1; if he learns to ride a bike by using a bike without training wheels, his probability of falling is 0.5, and if he uses a unicycle, his probability of falling is 0.8. Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.
a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?
b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?
Mathematics
1 answer:
Anestetic [448]3 years ago
7 0

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

P(B|A) = \frac{P(B)*P(A|B)}{P(A)}

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

So

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that P(B) = \frac{1}{3}

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that P(A|B) = 0.1

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667

So

P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that P(B) = 0.7

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that P(A|B) = 0.1

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25

So

P(B|A) = \frac{0.7*0.1}{0.25} = 0.28

28% probability that Benny was learning to ride a bike using the training wheels

You might be interested in
Estimate the value of<br>9304 ÷93 =​
LuckyWell [14K]

Answer:

100

Step-by-step explanation:

Round 9304 to 9300. 9300/93 is just 100 since 100 * 93 = 9300 (this is something easily recognizable).

6 0
3 years ago
Evaluate 4(x+3)(x+1)/(x+5)(x-5) for x =3. A. 3/2 B. -6 C. 6 D. -3/2
sergey [27]

Answer:

-6

Step-by-step explanation:

Reduce the expression by cancelling common factors

5 0
2 years ago
Yo i need answers asap if you want points tell me in the COMMENTS do not answer if you don't know or if you just want points. Th
MaRussiya [10]

Answer:

can i get some points?

Step-by-step explanation:

3 0
3 years ago
Ratio of boys to girls in a class of 27 is 1:2 how many boys will there be?
labwork [276]

Answer:

Ratio of boys is 13.5 i think

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Mary sews at a rate of 60 inches per hour. How many feet does she sew in a minute?
makvit [3.9K]

Answer:

B. 0.083 rounded to the nearest thousandth.

Step-by-step explanation:

It is known that 12 inches = 1 foot and

60 minutes = 1 hour

Since we want to covert from inches per hour to feet per minute, then we would change 60 inches to feet in 1 hour 2 minutes in divide.

If 12 inches = 1 foot, then

60 inches = 60/12 = 5 feet

Therefore, the number of feet that she sews in a minute is

5/60 = 0.083 feet per minute

She sews 0.083 feet per minute.

This is the full explanation for this question.

5 0
3 years ago
Other questions:
  • A number that has a digit in tenths place, hundredths place or beyond
    9·2 answers
  • A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. An
    5·2 answers
  • Graph each inequality.<br> y&lt;2x+4
    10·1 answer
  • Which of the following is the formula for the volume of a pyramid with base area B and height h?
    7·2 answers
  • A baseball team ordered 12 jerseys. Each jersey costs the same amount. The shipping cost for the jerseys was $3 and the total co
    6·1 answer
  • I Need help please I don’t understand this
    7·1 answer
  • What is the value of x?
    8·1 answer
  • A university lecture hall has 100 seats. During class, 30% of the seats are empty. How many students are attending class?
    6·2 answers
  • If a thousand computer is marked of 35% what is the sale price ​
    15·1 answer
  • So I know that this isn’t the kind of app I should be speaking about my problems but I just want to burst out into tears from ho
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!