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# The probability of snow for each of the next three days is $\frac{2}{3}$. What is the probability that it will snow at least once during tho

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The probability of snow for each of the next three days is . What is the probability that it will snow at least once during those three days? Express your answer as a common fraction.

Aug 9, 2021

#1
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Case 1: once: 2/3 * 1/3 * 1/3 * 3

Case 2: twice: 2/3 * 2/3 * 1/3 * 3 C 2

case 3: 3 times: (2/3)^3

2/27*3 + 4/27*3 + 8/27 = 6/27 + 12/27 + 8/27 = 26/27.

Aug 9, 2021
#2
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We could use Complementary Counting for this.

The probability that it will not slow at all is      $$\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$$

Then we minus the total by   $$\frac{1}{27}$$

$$1 - \frac{1}{27} = \frac{26}{27}$$

Aug 9, 2021
#3
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we got the same answer, in different ways :D

Guest Aug 9, 2021