Let S be a sample space of all 3X3 matrices with entries from the set {0,1}. Let the events E1 and E2 be given by E1={A∈S:detA=0} and E2={A∈S:sum of entries of A is 7} If a matrix is chosen at random from S , then the conditional probability 2P(E1/E2) equals----

n(S)=29=512E2 contains those matrices in which sum of entries is 7There will be 7 one’s , 2 zeroes n(E2)=9C2=36E1∩E2 contains those matrices in which 7 ones , 2 zeroesn(E1∩E2)=3C1×3C1×2=18P(E1/E2)=P(E1∩E2)P(E2)18/51236/512=12=0.50

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let S be a sample space of all 3X3 matrices with entries from the set {0,1}. Let the events $E_{1} a n d E_{2}$ be given by $E_{1} = {A \in S : \det A = 0}$ and $E_{2} = {A \in S : s u m o f e n t r i e s o f A i s 7}$ If a matrix is chosen at random from S , then the conditional probability 2 $P (E_{1} / E_{2})$ equals----

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$n (S) = 2^{9} = 512$

$E_{2}$ contains those matrices in which sum of entries is 7

There will be 7 one’s , 2 zeroes $n (E_{2}) = 9_{C_{2}} = 36$

$E_{1} \cap E_{2}$ contains those matrices in which 7 ones , 2 zeroes

$n (E_{1} \cap E_{2}) = 3_{C_{1}} \times 3_{C_{1}} \times 2 = 18$

$P (E_{1} / E_{2}) = \frac{P (E_{1} \cap E_{2})}{P (E_{2})}$

$\frac{18 / 512}{36 / 512} = \frac{1}{2} = 0.50$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!