Probability
Independent Events — Probability of One Appearing Without the Other
nta_pyq_2024_jan
Grade 12
Question:
Let Ajay will not appear in JEE exam with probability $p=\dfrac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $q=\dfrac{1}{5}$. Then the probability that Ajay will appear in the exam and Vijay will not appear is:
$\dfrac{9}{35}$
$\dfrac{18}{35}$
$\dfrac{24}{35}$
$\dfrac{3}{35}$
Step-by-Step Solution
Key Concept: $P(\bar{A})=2/7\Rightarrow P(A)=5/7$. $P(A\cap V)=1/5$. Required: $P(A\cap\bar{V})=P(A)-P(A\cap V)=5/7-1/5$.
$P(A)=5/7$. $P(A\cap\bar{V})=5/7-1/5=18/35$.
Correct Answer: 2