I don't understand this problem

Note: 1.8 = 9/5

Explanation:

This problem may be strangely worded, so I'll try to phrase it differently. That part will come in a later section below (specifically section 3).

For now, let's just find the probability of finding two white marbles if we replace the first marble chosen. We consider this a "replacement" situation.

We have 5 blue, 3 red and 2 white marbles. That means 5+3+2 = 10 total. The probability of picking white is 2/10 = 1/5. Since the first marble is replaced, the probability of picking white the second time is still 1/5.

The probability of picking two white marbles is (1/5)*(1/5) = 1/25 = 0.04 = 4%

Now let's consider a "no replacement" situation. We won't put the marble back, or we won't replace it with an identical copy. After the first marble is picked, we have 10-1 = 9 marbles left and 2-1 = 1 white marble left.

The probability of getting white on the second selection, after no replacement is made, is 1/9 instead of 2/10 = 1/5

The probability of getting two white marbles in this scenario is (2/10)*(1/9) = (2*1)/(10*9) = 2/90 = 1/45 = 0.0222 = 2.22% approximately

We can see that there is a difference in probabilities between "replacement" and "no replacement" when we pick two white marbles like this.

The fractional answer to the first section was 1/25. Let A = 1/25

The fractional answer to the second section was 1/45. Let B = 1/45

A and B are the probabilities for "replacement" vs "no replacement" in that order.

Your teacher wants to know how many times greater the value of A is compared to B.

In symbols, your teacher wants to know the value of k in the equation A = Bk

So...

A = Bk

1/25 = (1/45)k

1/25 = k/45

1*45 = 25*k

45 = 25k

25k = 45

k = 45/25

k = (9*5)/(5*5)

k = 9/5

k = 1.8

Either the fractional or decimal version of k would work as the answer. It might sound better if you go with the decimal version, though again, both values are equivalent.

The value of A is 1.8 times greater compared to the value of B.

there are no answer choices

step-by-step explanation: