Two friends A and B meet every weekend either at a party or at a Sports Club. The probability that they meet at Sports Club is 4/9. The probability that they will dine together at a party and at the Club are respectively 1/3 and 2/5. On a certain weekend the probability that they disperse without dine together

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{86}{135}$

$\frac{17}{27}$

$\frac{10}{27}$

$\frac{56}{135}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$E_{1} = A & B$ meet at a Party

$E_{2} = A & B$ meet at a Sport Club

$P (E_{1}) = \frac{5}{9} P (E_{2}) = \frac{4}{9}$

A=They will dine together

$\begin{array}{rcl} P (\frac{A}{E_{1}}) & = & \frac{1}{3} P (\frac{A}{E_{2}}) = \frac{2}{5} \\ P (A) & = & \frac{5}{9} \times \frac{2}{3} + \frac{4}{9} \times \frac{3}{5} = \frac{86}{135} \end{array}$

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET