Home
Class 12
MATHS
Let A(1), A(2), A(3) be 3 events related...

Let `A_(1), A_(2), A_(3)` be 3 events related to a random experiment. Under what conditions will the events be exhaustive and mutually exclusive ?

Text Solution

Verified by Experts

The correct Answer is:
`P(A_(1) cup A_(2) cup A(3))=1`
and `P(A_(1) cup A_(2) cup A_(3))=P(A_(1))+P(A_(2))+P(A_(3))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let A_(1), A_(2), A_(3) be 3 evets related to a random experiment Under what conditions will be exhaustive and mutually exclusive?

If A_(1), A_(2),..,A_(n) are any n events, then

In the random rxperiment of rolling an unbiased die, let A be the event of getting a digit less than 4 and B be then event of getting a digit greater than 3 , show that the events A and B are mutually exclusive and exhaustive.

Let E denote the random experimnet of rolling two unbiased dice and A and B are two events connected with E. The event A occur if the sum of the digits shown on the two dice is 7 while the event B occurs if at least one of the dice shows up a 4. show that the events A and B neither mutually exclusive nor exhaustive.

In the random experiment of drawing a card from a well shuffed pack of 52 cards, let A,B,C and D be the events that the drawn card is a club, a diamond , a heart and a spade respectively. Examine whether the events A,B,C and D are mutually exclusive and exhaustive.

Three unbaised coins are tossed simultaneously. Describe three events A, B and C which are mutually exclusive and exhaustive,

Let theta=(a_(1),a_(2),a_(3),...,a_(n)) be a given arrangement of n distinct objects a_(1),a_(2),a_(3),…,a_(n) . A derangement of theta is an arrangment of these n objects in which none of the objects occupies its original position. Let D_(n) be the number of derangements of the permutations theta . The relation between D_(n) and D_(n-1) is given by

Let A_(1), A_(2), A_(3), A_(4) be the areas of the triangular faces of a tetrahedron, and h_(1), h_(2), h_(3), h_(4) be the corresponding altitudes of the tetrahedron. If the volume of tetrahedron is 1//6 cubic units, then find the minimum value of (A_(1) +A_(2) + A_(3) + A_(4))(h_(1)+ h_(2)+h_(3)+h_(4)) (in cubic units).

Three unbaised coins are tossed simultaneously. Describe three events D, E and F which are mutually exclusive but not exhaustive

A_(1), A_(2) and A_(3) are three events. Show that the simultaneous occurrence of the events is P(A_(1) cap A_(2) cap A_(3))=P(A_(1))P(A_(2)//A_(1))P[A_(3)//(A_(1) cap A_(2))] State under which condition P(A_(1) cap A_(2) cap A_(3))=P(A_(1))P(A_(2))P(A_(3))