wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution

Sample space S=29
P(E1|E2)=P(E1E2)P(E2)
E2:Sum of entries of A is 7 i.e matrix consist of 7 ones and 2 zeros
such as ∣ ∣111111100∣ ∣
n(E2)=9!7!2!=8×92=36
For det A to be zero, both zero should be in same row or same column
Therefore, for selecting 2 zero in same row from 3 row matrix =3×3C2=3×3=9
Similary for selecting 2 zero in same column from 3 column matrix=3×3C2=3×3=9
So, n(E1E2)=9+9=18
P(E1|E2)=P(E1E2)P(E2)=1836=12=0.5

flag
Suggest Corrections
thumbs-up
10
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Conditional Probability
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon