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Alexxandr [17]
3 years ago
13

Kirby made contributions to roth ira

Mathematics
1 answer:
yawa3891 [41]3 years ago
6 0
Details? you need to add the whole question
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A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra
VMariaS [17]

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

8 0
3 years ago
pete is a furniture refinisher. to paint a chest of drawers, he needs 1/2 gallon of paint. he has 1 quart. how many more quarts
bezimeni [28]
Pete needs one more quart of paint, leaving two quarts in total.
7 0
3 years ago
5-star rating and brainiest
Lelu [443]

Answer:

Step-by-step explanation:

What to do??

8 0
3 years ago
Read 2 more answers
You need at least 30 cubic feet of sand to fill a sand box. Each box contains 2.5 cubic feet of sand. Write and solve an inequal
BabaBlast [244]

Answer:

2.56 = 30

b = 12

(Sorry if I’m wrong! I speeded on it.)

Step-by-step explanation:

6 0
3 years ago
Brianna and Holden hiked 6 2/9 miles on Monday and 2 2/3 miles on Tuesday. How many times as far did they hike on Monday as they
spin [16.1K]

Answer:

  2 1/3 times as far

Step-by-step explanation:

The ratio of distances is ...

  (Monday distance) / (Tuesday distance) = (6 2/9)/(2 2/3)

  = (56/9)/(8/3) = (56·3)/(8·9) = 7/3 = 2 1/3

They hiked 2 1/3 times as far on Monday as they did on Tuesday.

6 0
3 years ago
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