Question

There is a boardwalk game at Point Pleasant where you are blindfolded to throw darts at a board full of balloons. Each time a dart is popped, it is not replaced until the next turn. The board has 10 green,4 purple,5 red,and 2 tiedye and 3 black balloons.
Find the probabilities of the following outcomes:
a. Popping two reds consecutively during one turn
b. Popping a red, then a green during one turn
c. Popping a red, then a black, then a red during one turn
d. Popping anything but a tiedyed balloon on three consecutive throws

Answer 1

The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;

a. 5/138

b. 25/276

c. 5/1012

d. 35/46

How can the different probabilities be calculated mathematically?

Given parameters;

Number of balls;

Green = 10

Purple = 4

Red = 5

Tie-dye = 2

Black = 3

Mode of selection = Without replacement

Number of balloons = 10+4+5+2+3 = 24

a. Probability of popping a red balloon = 5/24

Probability of popping a second red balloon = 4/23

Therefore;

Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138

b. Probability of popping a red balloon = 5/24

Probability of popping a green balloon next = 10/23

Therefore;

Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276

c. Probability that the first balloon that pops is a red = 5/24

Next balloon is a black = 3/23

Third balloon is red = 4/22

The probability, P, is therefore;

• P = 5/24 × 3/23 × 4/22 = 5/1012

d. The probability that the first balloon is a tie-dye = 2/24 = 1/12

Therefore;

Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12

Probability that the second balloon is not a tie-dye = 21/23

Similarly;

Probability that the third balloon is not a tie-dye = 20/22 = 10/11

Which gives;

The probability, P, of popping anything but a tie-dye on three consecutive throws is therefore;

• P = 11/12 × 21/23 × 10/11 = 35/46

Learn more about probability theory in mathematics?

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