Probability: One at a Time - Outcome A AND Outcome B = Multiply Probabilities
The probability of rain in Barcelona on any given day is 0.4. What is the probability that it will rain on exactly one of three consecutive days in Barcelona?
Incorrect.
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Correct.
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Note that if the probability of rain is 0.4, then the probability of no rain on any given day is $$1 - 0.4 = 0.6$$ because
>Probability of $$x$$ _not_ happening $$= 1 -$$ Probability of $$x$$ happening.
There are three "good" scenarios to consider:
1) There is rain on the first day and no rain on the other days:
>>$$\text{Probability of RNN} = \frac{4}{10}\times\frac{6}{10}\times\frac{6}{10}
=\frac{144}{1{,}000}=0.144$$
2) There is rain on the second day and no rain on the other days.
>>$$\text{Probability of NRN} = \frac{6}{10}\times\frac{4}{10}\times\frac{6}{10}
=\frac{144}{1{,}000}=0.144$$
3) There is rain on the third day and no rain on the other days.
>>$$\text{Probability of NNR} = \frac{6}{10}\times\frac{6}{10}\times\frac{4}{10}
=\frac{144}{1{,}000}=0.144$$
Thus, the total probability is
>$$\text{Total Probability} = 0.144+0.144+0.144 = 0.432$$.
Incorrect.
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Incorrect.
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Incorrect.
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0.072
0.144
0.288
0.432
0.720
