Question

problem solving

1. your dart is equally likely to hit any point inside the board shown. you throw a dart and pop a balloon. what is the probability that the balloon is red or blue? (see example 1)

Explanation:

Step1: Count total balloons

Count all balloons in the dartboard. Let's list them row by row:

• Row 1: 5 balloons (blue, red, green, red, yellow)
• Row 2: 5 balloons (green, yellow, red, green, red)
• Row 3: 5 balloons (red, green, blue, green, yellow)
• Row 4: 5 balloons (green, yellow, red, green, blue)

Wait, actually, looking at the image: Let's count again carefully. Let's count each balloon:

First row (top): blue (1), red (1), green (1), red (1), yellow (1) → 5

Second row: green (1), yellow (1), red (1), green (1), red (1) → 5

Third row: red (1), green (1), blue (1), green (1), yellow (1) → 5

Fourth row: green (1), yellow (1), red (1), green (1), blue (1) → 5

Wait, no, maybe the image has 4 rows? Wait, the image shows:

First row (top): 5 balloons (blue, red, green, red, yellow)

Second row: 5 balloons (green, yellow, red, green, red)

Third row: 5 balloons (red, green, blue, green, yellow)

Fourth row: 5 balloons (green, yellow, red, green, blue) → No, that's 20? Wait, no, maybe I miscounted. Let's count the number of each color:

Red balloons: Let's see. First row: 2 (red, red? Wait first row: blue, red, green, red, yellow → 2 red. Second row: red, red → 2. Third row: red → 1. Fourth row: red → 1. Wait no, let's look at the image again. The dartboard has:

First row (top): blue (1), red (1), green (1), red (1), yellow (1) → red: 2

Second row: green (1), yellow (1), red (1), green (1), red (1) → red: 2

Third row: red (1), green (1), blue (1), green (1), yellow (1) → red: 1

Fourth row: green (1), yellow (1), red (1), green (1), blue (1) → red: 1

Total red: 2 + 2 + 1 + 1 = 6

Blue balloons: First row: 1, third row: 1, fourth row: 1 → total 3

Green balloons: First row: 1, second row: 2, third row: 2, fourth row: 2 → 1+2+2+2=7

Yellow balloons: First row:1, second row:1, third row:1, fourth row:1 → 4

Total balloons: 6 (red) + 3 (blue) + 7 (green) + 4 (yellow) = 20. Let's check: 6+3=9, 9+7=16, 16+4=20. Correct.

Step2: Count red or blue balloons

Red balloons: 6, blue balloons: 3. Since red and blue are mutually exclusive (a balloon can't be both red and blue), the number of red or blue balloons is 6 + 3 = 9.

Step3: Calculate probability

Probability is (number of favorable outcomes) / (total number of outcomes). So probability = 9 / 20.

Answer:

$\frac{9}{20}$