Options D and E should appear as shown below:
BTGmoderatorLU wrote:Source: Veritas Prep
If there is a 20% chance of rain every day for the next 7 days, what is the probability that it will rain exactly 2 days out of the next 7 days?
$$A. \ \frac{21}{10^7}$$
$$B.\ \frac{2^7}{10^7}$$
$$C.\ \frac{21^7}{10^7}$$
$$D.\ \frac{21\cdot2^{17}}{10^7}$$
$$E.\ \frac{42\cdot2^{17}}{10^7}$$
P(exactly n times) = P(one way) * all possible ways.
Let R = rain and N = no rain.
Since P(R) = 20% = 2/10, P(N) = 80% = 8/10 = 2³/10.
P(one way):
One way to get exactly 2 days of rain is to have rain on the first 2 days but not on the last 5 days.
P(RRNNNNN) = 2/10 * 2/10 * 2³/10 * 2³/10* 2³/10 * 2³/10 * 2³/10 = 2¹�/10�.
All possible ways:
Any arrangement of the letters RRNNNNN will yield exactly 2 days of rain.
Thus, to account for all the ways to get exactly 2 days of rain, the result above must be multiplied by the number of ways to arrange RRNNNNN.
Number of ways to arrange RRNNNNN = 7!/(2!5!) = 21.
Multiplying the results above, we get:
P(exactly 2 days of R) = (21 * 2¹�)/10�.
The correct answer is
D.
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