1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider two sets P = a , b , c , d , e and Q = f , g , h , i , j A person selects a set P with probability 1 / 3 or set Q with probability 2 / 3 and forms a subset R of two elements both selected from set P or Q. Find probability that set R consists of one vowel one consonants

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider two sets $P =\{ a , b , c , d , e \}$ and $Q =\{ f , g , h , i , j \} A$ person selects a set $P$ with probability $1 / 3$ or set $Q$ with probability $2 / 3$ and forms a subset $R$ of two elements both selected from set $P$ or $Q$. Find probability that set $R$ consists of one vowel $\&$ one consonants

Probability - Part 2

Solution:

$P(R)=P(P) \cdot P\left(\frac{V . C}{P}\right)+P(Q) \cdot P\left(\frac{V . C}{Q}\right)$
$=\frac{1}{3} \times \frac{{ }^2 C_1 \cdot{ }^3 C_1}{{ }^5 C_2}+\frac{2}{3} \cdot \frac{{ }^1 C_1{ }^4 C_1}{{ }^5 C_2}$
$=\frac{1}{3} \times \frac{6}{10}+\frac{2}{3} \times \frac{4}{10}=\frac{6+8}{30}=\frac{7}{15}$