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
choli [55]
3 years ago
7

A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra

wing the second one). What is the probability that both marbles are blue? What is the probability that both marbles are yellow? What is the probability of one blue and then one yellow? If you are told that both selected marbles are the same color, what is the probability that both are blue?
Mathematics
1 answer:
VMariaS [17]3 years ago
8 0

Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

53.33% probability of one blue and then one yellow

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that N = 6

4 blue, which means that k = 4

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that N = 6

2 yellow, which means that k = 2

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that P(A) = 0.4 + 0.0667 = 0.4667

Probability of both being the same color and blue:

40% probability that both are blue, which means that P(A \cap B) = 0.4

Desired probability:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

You might be interested in
Need help ASAP! ——————————————————————————————
Taya2010 [7]

Answer:wanted to help but not that smart

Step-by-step explanation:

4 0
3 years ago
Given f(x) = -* -<br> - 5, solve for x when f(x) = -3.
Ne4ueva [31]

Answer:

x = -2

Step-by-step explanation:

Step 1: Define

f(x) = -x - 5

f(x) = -3

Step 2: Substitute and Evaluate

-3 = -x - 5

2 = -x

x = -2

7 0
3 years ago
Read 2 more answers
Interpret the average rate of change of -14/3 that
Jobisdone [24]

Answer:

On average, the slide drops 14 feet for every 3 feet of horizontal distance.

On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.

5 0
3 years ago
Write the word sentence as an equation.<br> The quotient of two times a number k and -2.6 is 12\
MArishka [77]
2k/-2.6=12 is the word sentences as an equation
5 0
3 years ago
A wire 4 1/2 feet long is being cut into smaller pieces of wire, each 11/4 feet long. What is the maximum number of the smaller
Goryan [66]

Answer:

1

Step-by-step explanation:

Take 4 1/2 and turn it into just halves by multiplying 4•2 and then adding it to one. 9/2 then multiply that by 2 because you need the denominator to be 4 getting 18/4. Then subtract 11/4 you end up getting 9/4. So technically you have 2 pieces but if you want them both to be 11/4 you only have one

4 0
3 years ago
Other questions:
  • Need some help asap thanks!
    11·1 answer
  • Mr.Joseph recently received a notice that his average gas and electric bill would increase at the beginning of the year. He went
    7·1 answer
  • Review the graph of function h(x). Which point is on the graph of the inverse function h–1(x)?
    11·1 answer
  • There are 24 more trucks than twice the number of cars for sale at a dealership. If there are 100 trucks for sale, how many cars
    15·2 answers
  • 3. Solve the equation below for X<br> 9 ( X- 5) = 4x – 5<br><br> A 8<br> B 10<br> C-8<br> D-10
    15·2 answers
  • An artist designed a badge for a school club. Figure ABCD on the coordinate grid
    7·2 answers
  • 35 points!!! Which is the general form of the equation of the circle shown?
    10·2 answers
  • Henry made a scale model of a submarine. The submarine has an actual height of 75 feet. Henry’s model used a scale in which 1 in
    13·1 answer
  • PLEASE HELP ME.<br><br> Is the point (3,-2) on the graph of 3x – 2y = 12?
    12·1 answer
  • I SWEAR IF I GET ANOTHER LINK I WILL SCREAM Parth created a Box-and-Whisker Plot to show the average weight of the fish he caugh
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!