Home
Class 12
MATHS
There are n turns each continuous (n+1) ...

There are n turns each continuous (n+1) balls such that the ithurn contains 'I' white balls and (n+1-i) red balls. Let `u_(1)` be the event of selecting ith urn, i=1,2,3……..n and W denotes the event of getting a white balls.
If ` P(u_(i)) prop i`, where i=1,2,3,........,..n, then `lim_(n to oo) P(W)` is equal to

A

1

B

`(2)/(3)`

C

`(1)/(4)`

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `P(u_(i))=ki,Sigma P(u_(i))=1`
`rArr K=(2)/(n(n+1))`
`underset(nrarroo)limP(W)=underset(nrarroo)lim sum _(i=1)^(n)(2i^(2))/(n(n+1)^(2))`
`=underset(nrarroo)lim(2n(n+1)(2n+1))/(6n(n+1)^(2))=(2//3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let H_1, H_2, , H_n be mutually exclusive and exhaustive events with P(H_i)>0,i=1,2,...,n. Let E be any other event with 0 P(E|H_i .P(H_i) for i=1,2,.......,n statement II sum_(i=1)^n P(H_i)=1

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n) is equal to

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.

Each of the n urns contains 4 white and 6 black balls. The (n+1) th urn contains 5 white and 5 black balls. One of the n+1 urns is chosen at random and two balls are drawn from it without replacement. Both the balls turn out to be black. If the probability that the (n+1) th urn was chosen to draw the balls is 1/16, then find the value of n .

An urn containsf 10 red and 8 white balls. Write sample space S and n(S). Write the events A and B using set form and mention n(A) and n(B) if A is the event that bell is while, B is the event that ball is neither white nor red.

There are (n + 1) white and (n + 1) black balls, each set numbered 1 to n + 1. The number of ways in which the balls can be arranged in a row so that adjacent balls are of different colours, is

There are two urns Aa n dB . Urn A contains 5 red, 3 blue and 2 white balls, urn B contains 4 red, 3 blue, and 3 white balls. An urn is chosen at random and a ball is drawn. Probability that ball drawn is red is a. 9//10 b. 1//2 c. 11//20 d. 9//20

Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes denoted by n_(i) , the label of the ball drawn from the i^(th) box, (I = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n_(1) lt n_(2) lt n_(3) is

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.Given that the drawn ball from U2 is white, the probability that head appeared on the coin