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Question: Answered & Verified by Expert
There is $25 \%$ chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of 7 days?
MathematicsProbabilityNDANDA 2016 (Phase 2)
Options:
  • A $1-\left(\frac{1}{4}\right)^{7}$
  • B $\left(\frac{1}{4}\right)^{7}$
  • C $\left(\frac{3}{4}\right)^{7}$
  • D $1-\left(\frac{3}{4}\right)^{7}$
Solution:
2094 Upvotes Verified Answer
The correct answer is: $1-\left(\frac{3}{4}\right)^{7}$
The probability of rain in one day
$=\frac{25}{100}=\frac{1}{4}$
Probability of getting at least one rainy day within a period of 7 days
$=1-\left[1-\frac{1}{4}\right]^{7}=1-\left[\frac{3}{4}\right]^{7}$

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