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
<h3>How can the different probabilities be calculated mathematically?</h3>
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, <em>P</em>, 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, <em>P</em>, 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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