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Bismuth83
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Julia is about to draw a marble from a bag that contains red, white, a 19 May 2025, 21:52
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Number of
Marbles: 40 Probability of
Red (in %): 50
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25% (medium)

Question Stats:

76% (01:53) correct 24% (02:04) wrong based on 420 sessions

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Julia is about to draw a marble from a bag that contains red, white, and blue marbles. Currently there are 10 red marbles, 20 white marbles, and 30 blue marbles, and Julia would like to draw a red marble. From the table below, select the number of red marbles that would have to be added to the bag in order to reach the new probability of Julia drawing a red marble.
Number of
Marbles 		Probability of
Red (in %)
10
20
30
40
50
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Number of
Marbles: 40 Probability of
Red (in %): 50
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Julia is about to draw a marble from a bag that contains red, white, a 20 May 2025, 01:20
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solution:

We have already been given 10 Red, 20 White, and 30 Blue marbles. So, the total number would be 60. Currently, the probability of red marbles is \(\frac{10}{60}\) = \(\frac{1}{6}\). Now, we can check the new probability of Julia drawing a red marble by checking against the percentage given to us. Let's consider the new value added to this, which is x. Since we are not told how much new value is to be added to get to the solution.

1.\(\frac{ (10 + x)}{(60 + x) }\)= 10% (Not possible)

2.\( \frac{(10 + x)}{(60 + x)}\) = 20% (Not possible)

3.\( \frac{(10 + x)}{(60 + x) }\)= 30% (Not possible)

4.\( \frac{(10 + x)}{(60 + x) }\)= 40%(Not possible)

5.\(\frac{ (10 + x)}{(60 + x)}\) = 50% (possible). Here, we will get the value for x as 40. So, the number of red marbles that should be added is 40, and 50% is our new probability.
Bismuth83
Julia is about to draw a marble from a bag that contains red, white, and blue marbles. Currently there are 10 red marbles, 20 white marbles, and 30 blue marbles, and Julia would like to draw a red marble. From the table below, select the number of red marbles that would have to be added to the bag in order to reach the new probability of Julia drawing a red marble.
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Julia is about to draw a marble from a bag that contains red, white, a 21 May 2025, 07:36
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Bismuth83, can you provide the OA?
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Julia is about to draw a marble from a bag that contains red, white, a Updated on: 03 Jul 2025, 11:12
Originally posted by Bismuth83 on 03 Jul 2025, 11:11.
Last edited by Bismuth83 on 03 Jul 2025, 11:12, edited 2 times in total.
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1. The question asks us to find a working pair of number of added red marbles and the probability of picking one.

2. First of all, let the number of new red marbles be equal to n. Now let's write out the probability of choosing a red marble (P), \(P = \frac{# \ of \ red \ marbles}{ # \ of \ all \ marbles} = \frac{# \ of \ old \ red \ marbles + # \ of \ new \ red \ marbles}{(# \ of \ old \ red \ marbles + # \ of \ new \ red \ marbles) + # \ of \ white \ marbles + # \ of \ blue \ marbles} = \)
\( = \frac{10 + n}{(10 + n) + 20 + 30} = \frac{10 + n}{60 + n}\).

3. Since there is no other information, let's compare P to possible probabilities.

- \(P = 10\% \rightarrow \frac{10 + n}{60 + n} = 0.1 \rightarrow 10 + n = 6 + 0.1n \rightarrow 0.9n = -4 \rightarrow n \approx -4.4\), which doesn't work.
- \(P = 20\% \rightarrow \frac{10 + n}{60 + n} = 0.2 \rightarrow 10 + n = 12 + 0.2n \rightarrow 0.8n = 2 \rightarrow n = 2.5\), which doesn't work.
- \(P = 30\% \rightarrow \frac{10 + n}{60 + n} = 0.3 \rightarrow 10 + n = 18 + 0.3n \rightarrow 0.7n = 8 \rightarrow n \approx 11.4\), which doesn't work.
- \(P = 40\% \rightarrow \frac{10 + n}{60 + n} = 0.4 \rightarrow 10 + n = 24 + 0.4n \rightarrow 0.6n = 14 \rightarrow n \approx 23.3\), which doesn't work.
- \(P = 50\% \rightarrow \frac{10 + n}{60 + n} = 0.5 \rightarrow 10 + n = 30 + 0.5n \rightarrow 0.5n = 20 \rightarrow n = 40\), which works.

4. Our answer will be: Number of Marbles - 40 and Probability of Red (in %) - 50.
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