Question

1. a single marble is drawn from a jar containing 20 marbles, as shown below: 3a what is the probability of drawing a blue marble? express your answer as a percentage. probability = enter your next step here

Explanation:

Step1: Count blue marbles

Looking at the jar, count the blue (●) marbles. Let's see: first row (after red/black) has 2, next row 1, then 2, then 1? Wait, let's list:

First blue row (second row): 2 blue.

Third row: 1 blue (middle).

Fourth row (wait, let's count properly. Let's list all blue marbles:

- Row 2 (from top, after red/black): 2 blue (positions 2,3)
- Row 3: 1 blue (position 2)
- Row 5 (wait, maybe better to count: let's see the blue marbles:

Looking at the image:

Blue marbles: let's count:

First blue group: 2 (top blue row)

Then 1 (middle blue in black row)

Then 2 (blue in the row with red)

Then 1 (blue in the bottom row with red/black)

Wait, maybe better: let's count total blue marbles. Let's see:

From the image, let's count:

- Blue marbles: let's see, the blue ones:

First, the two blue in the second row (top after red/black).

Then one blue in the third row (middle of black row).

Then two blue in the fifth row (with red).

Then one blue in the sixth row (bottom row with red/black). Wait, no, maybe I miscounted. Wait, let's do it step by step.

Wait, the jar has 20 marbles. Let's count blue, red, black.

Red marbles: let's count. Red marbles: top left (1), then a red in the fourth row (1), then bottom left (1), bottom right (1), and the red in the middle row (1)? Wait, no, let's count red:

Top: 1 red (left)

Then a red in the fourth row (middle)

Then bottom left (1), bottom right (1), and the red in the third row (right)? Wait, maybe red marbles: 1 (top left) + 1 (middle row) + 1 (bottom left) + 1 (bottom right) + 1 (third row right)? Wait, no, the image shows:

Red marbles: let's see:

- Top row: 1 red (left)

- Fourth row (from top): 1 red (middle)

- Fifth row (from top): 1 red (left), 1 red (right)? Wait, no, the fifth row (the row with blue and red) has 1 red (middle) and two blue? Wait, maybe I'm overcomplicating. Let's use the formula: probability = (number of blue marbles) / total marbles * 100.

Total marbles: 20.

Let's count blue marbles:

Looking at the image:

- Second row (top blue row): 2 blue.

- Third row: 1 blue (middle of black row).

- Fifth row (with red): 2 blue (left and right of red).

- Sixth row (bottom row with red/black): 1 blue (middle).

Wait, that's 2 + 1 + 2 + 1 = 6? Wait, no, maybe:

Wait, let's count again. Let's list all blue marbles:

1. Top blue row (second row): 2 (positions 2,3)

2. Third row (black row): 1 (position 2)

3. Fifth row (red in middle, blue on left and right): 2 (positions 1,3)

4. Sixth row (bottom row, red on left and right, blue in middle): 1 (position 2)

So total blue marbles: 2 + 1 + 2 + 1 = 6? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, let's count black marbles.

Black marbles: top row: 2 (middle and right).

Third row: 2 (left and right of blue).

Fourth row: 2 (left and middle of red).

Fifth row: 1 (right of blue).

Sixth row: 1 (middle of red). Wait, no, black marbles:

Top row: 2 black (middle, right)

Third row: 2 black (left, right)

Fourth row: 2 black (left, middle)

Fifth row: 1 black (right)

Sixth row: 1 black (middle)

So black marbles: 2 + 2 + 2 + 1 + 1 = 8?

Red marbles: top row: 1 (left)

Fourth row: 1 (middle)

Sixth row: 2 (left, right)

Fifth row: 1 (middle)

Wait, red marbles: 1 + 1 + 2 + 1 = 5?

Then blue marbles: total 20 - 8 (black) - 5 (red) = 7? Wait, 8 + 5 = 13, 20 -13=7? No, 8+5=13, 20-13=7? Wait, maybe.

Wait, let's check:

If black is 8, red is 5, then blue is 20 -8 -5=7?

Wait, but let's count blue again. Let's see:

Blue marbles:

- Second row (top blue): 2

- Third row (black row): 1

- Fifth row (with red): 2

- Sixth row (bottom row): 2? Wait, no, maybe I miscounted black.

Wait, top row: 1 red, 2 black.

Second row: 2 blue.

Third row: 2 black, 1 blue.

Fourth row: 2 black, 1 red.

Fifth row: 2 blue, 1 red.

Sixth row: 2 red, 1 blue, 1 black? Wait, no, the bottom row (sixth row) has: left red, middle blue, right red, and a black? Wait, no, the bottom row (sixth row) has: left red, middle blue, right red, and a black? Wait, no, the jar has 20 marbles, so let's count rows:

Row 1 (top): 1 red, 2 black (total 3)

Row 2: 2 blue (total 2)

Row 3: 2 black, 1 blue (total 3)

Row 4: 2 black, 1 red (total 3)

Row 5: 2 blue, 1 red (total 3)

Row 6: 2 red, 1 blue, 1 black (total 4)

Wait, 3+2+3+3+3+4=18? No, that's not 20. So my row counting is wrong.

Alternative approach: total marbles 20. Let's count blue marbles correctly.

Looking at the image (as per the problem), let's count blue marbles:

- Blue marbles: let's see, the blue ones are:

1. Top blue row: 2

2. Middle blue (in black row): 1

3. Blue in the row with red (two blue, one red): 2

4. Blue in the bottom row (with red and black): 1

Wait, that's 2+1+2+1=6? No, maybe 5? Wait, no, let's use the formula.

Wait, maybe the blue marbles are 5? No, let's do it properly.

Wait, the problem says 20 marbles. Let's count:

Red marbles: let's count. Red marbles: top left (1), then a red in the middle (1), then bottom left (1), bottom right (1), and the red on the right in the third row (1). So 5 red marbles.

Black marbles: top two (1,2), then third row two (1,2), fourth row two (1,2), fifth row one (1), and bottom one (1). So 2+2+2+1+1=8 black marbles.

Then blue marbles: 20 -5 -8=7. Ah, 20-5-8=7. So blue marbles:7.

So probability of drawing blue is (7/20)*100.

Step2: Calculate probability as percentage

Probability = (number of blue marbles / total marbles) * 100

Number of blue marbles =7, total=20.

So (7/20)*100 = 35.

Wait, 7 divided by 20 is 0.35, times 100 is 35. So 35%.

Wait, let's confirm: 7/20 = 0.35, 0.35*100=35. So the probability is 35%.

Answer:

35%