Advertisements
Advertisements
प्रश्न
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
उत्तर
Case 1 : 1 girl + 3 boys = ` ""^6C_1 xx ""^8C_3`
Case 2 : 2 girl + 2 boys = ` ""^6C_2 xx ""^8C_2`
Case 3 : 3 girl + 1 boys = ` ""^6C_3 xx ""^8C_1`
Case 4 : 4 girl + 0 boys = ` ""^6C_4 xx ""^8C_0`
Required probability = `( ""^6C_3 xx ""^8C_1)/(""^14C_4) + ( ""^6C_4 xx ""^8C_0)/(""^14C_4)`
= `(160)/(1001) + (15)/(1001) = (175)/(1001)`
= `(25)/(143) = 0.1748`
APPEARS IN
संबंधित प्रश्न
There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.
A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?
A fair coin is tossed 8 times, find the probability of at least six heads
Find the probability of 4 turning up at least once in two tosses of a fair die.
A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?
An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) The number of red balls and green balls is equal.
One dialing certain telephone numbers assume that on an average, one telephone number out of five is busy, Ten telephone numbers are randomly selected and dialed. Find the probability that at least three of them will be busy.
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in head, a die thrown, otherwise a coin is tossed.
Find total number of distinct possible outcomes n(S) of the following random experiment.
5 balls are randomly placed into 5 cells, such that each cell will be occupied.
Two dice are thrown. Write favourable Outcomes for the following event.
P: Sum of the numbers on two dice is divisible by 3 or 4.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events P and Q are mutually exclusive and exhaustive.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is not taken into account.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is taken into account.
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, ...., n}. Find P[r ≤ p|s ≤ p], where p ∈ S.
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a white ball is selected?
By examining the chest X ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In a certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is ______.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ______.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is ______.
A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either ace or a king?
Three horses A, B, Care in a race. A is twice as likely to win as B, and B is twice as likely to win as C. The probability that C wins, P(C) is
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
