Question

Weather forecast made for $30$ days in a month was recorded and found that it was correct for $21$ days. What is the probability that on a randomly selected day, the forecast is i) correct and ii) not correct?

Answer 1

Total no. of days the weather forecast took place $=30$

$\Rightarrow$ Total no. of days that the forecast came true $=21$

$\Rightarrow$ No. of days the forecast came wrong $=9.$

$1.)P$ (Correct) $={}^{21}{C}_1{}^{30}{C}_1=\frac{21}{30}=\frac{7}{10}.$

$2.)P$ ( Not Correct) $={}^9{C}_1{}^{30}{C}_1=\frac{9}{30}=\frac{3}{10}.$

Hence, solved.