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
Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.
ollegr [7]

Answer:

a(1)= -3

a(n)=a(n-1) (-3)

Step-by-step explanation:

hope this helps

8 0
3 years ago
On Monday, the high was 60oF. On Tuesday, the high was 10% more than Monday. Then on Wednesday, the temperature decrease by 8%.
Arada [10]

Answer:

60.72

Step-by-step explanation:

Monday: 60 degrees

Tuesday: temperature increases by 10 percent

60 + 10% of 60

60 + .10*60 = 70 +6 = 66

Wednesday: temperature decreases by 8 percent

66 - 8%of 66

66 - .08*66 = 66 -5.28=60.72

7 0
3 years ago
Read 2 more answers
What is 9| - z/3| + 6 < 30
Reil [10]
9|⁻¹/₃z| + 6 < 30
9|⁻¹/₃z| + 6 < ±30
9|⁻¹/₃z| + 6 < 30    or    9|⁻¹/₃z| + 6 > -30
9(¹/₃z) + 6 < 30    or    9(¹/₃z) + 6 > -30
     3z + 6 < 30       or       3z + 6 > -30
           - 6   - 6                       - 6     - 6
           3z < 24          or          3z > -24
            3      3                         3       3
             z < 8            or            z > -8

Solution Set: {z|z < 8 or z > -8} and (-∞, 8) or (-8, ∞)
4 0
3 years ago
Read 2 more answers
Find the greatest common factor of 28a^5 46a^3
Tasya [4]
The answer to the question

4 0
3 years ago
A student thinks that (1, 2) is a solution to y = 2x - 3. While checking the solution, the student gets 1 = 2(2) -3. What error
BabaBlast [244]
He put in the value of x into y
and the value of y in x
if that confuse you here this is what it will look like
(x,y)->(y,x)
6 0
3 years ago
Other questions:
  • We wish to construct a 90% confidence interval on the mean of a population known to be normally distributed based on a sample of
    12·1 answer
  • Simplify: 6 to the the 6th power multiplied by 6 to the second power​
    10·1 answer
  • What is the prime factorization of 1,575 (with work)
    6·2 answers
  • What is the approximate value of f(5) for the function f(x)=6.87(2.5)(x – 1)?
    14·1 answer
  • If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in 5 years?
    10·1 answer
  • Which describes Myra's distance as time increases?
    5·2 answers
  • I NEED HELP ILL GIVE TONS OF POUNTS find the mean of the data in the pictograph below​
    9·2 answers
  • CAN ANYONE HELP MY GRADES ARE KINDA LOW AND I NEED TO SLOVE THIS SO I CAN BOOST UP MY GRADES
    5·1 answer
  • Consider the graph of the parent exponential function fand transformed function g.
    11·1 answer
  • What is equivalent to (9f + 12)*4)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!