Answer to Question #216196 in Statistics and Probability for Muniru

Question

If sample space S={e1,e2,e3,e4}, find P(e1) if P(e2)=1/5 and P(e3)=1/3

Answer 1

$S=\{e_1,e_2,e_3,e_4\}$

Given,

$P(e_2)=1/5\\P(e_3)=1/3$

and we know that

$P(e_1)+P(e_2)+P(e_3)+P(e_4)=1\\\ \\\implies P(e_1)+\dfrac{1}{5}+\dfrac{1}{3}+P(e_4)=1\\\ \\\implies P(e_1)+P(e_4)=1-\dfrac{1}{5}-\dfrac{1}{3}=\dfrac{7}{15}$

Let $P(e_4)=\dfrac{1}{15}$

So, $P(e_1)=\dfrac{7}{15}-\dfrac{1}{15}=\dfrac{6}{15}$