Question

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?

• A. $1-{\left(\frac{1}{4}\right)}^7$
• B. ${\left(\frac{1}{4}\right)}^7$
• C. ${\left(\frac{3}{4}\right)}^7$
• D. $1-{\left(\frac{3}{4}\right)}^7$

Answer 1

The correct option is D $1-{\left(\frac{3}{4}\right)}^7$

Let p be the probability that it rains on a particular day.

$p=25\%=\frac{1}{4}$

Probability that there is at least 1 rainy day within a period of 7 days

$=1-$ Probability that there is no rainy day within a period of 7 days

$=1{-}^7{C}_0{p}^0(1-p{)}^7$

$=1-{(1-\frac{1}{4})}^7$

$=1-{\left(\frac{3}{4}\right)}^7$

Answer is option (D)