Advertisements
Advertisements
प्रश्न
n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
उत्तर
It is given that n (≥ 3) persons are seated in a row and two persons are selected.
∴ Total number of elementary event = n(S) = nC2
Let E be the event associated with the experiment that two persons are together.
∴ n(E) = n -1C1
Thus, required probability = P(E) = \[\frac{n(E)}{n(S)}\]
= \[\frac{^{n - 1}{}{C}_1}{^{n}{}{C}_2}\]
= \[\frac{\left( n - 1 \right)}{\frac{n\left( n - 1 \right)}{2}} = \frac{2\left( n - 1 \right)}{n\left( n - 1 \right)} = \frac{2}{n}\]
APPEARS IN
संबंधित प्रश्न
Describe the sample space for the indicated experiment: A die is thrown two times.
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
If a coin is tossed two times, describe the sample space associated to this experiment.
Write the sample space for the experiment of tossing a coin four times.
Two dice are thrown. Describe the sample space of this experiment.
A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of elementary events associated to this experiment.
An experiment consists of boy-girl composition of families with 2 children.
What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
An experiment consists of boy-girl composition of families with 2 children.
What is the sample space if we are interested in the number of boys in a family?
Three coins are tossed once. Describe the events associated with this random experiment:
A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(ii) Which events are elementary events?
Three coins are tossed once. Describe the events associated with this random experiment:
A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(iii) Which events are compound events?
A card is picked up from a deck of 52 playing cards.
What is the sample space of the experiment?
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a jack, queen or a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not a black card.
A bag contains 6 red, 4 white and 8 blue balls. if three balls are drawn at random, find the probability that one is red, one is white and one is blue.
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:
(i) just one ace
20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is odd?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has at most one girl?
Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
What is the probability that a leap year will have 53 Fridays or 53 Saturdays?
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
What is the probability that the 13th days of a randomly chosen month is Friday?
Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral.
If A and B are two independent events such that \[P (A \cap B) = \frac{1}{6}\text{ and } P (A \cap B) = \frac{1}{3},\] then write the values of P (A) and P (B).
A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
What is the probability that a randomly chosen two-digit positive integer is a multiple of 3?
A typical PIN (personal identification number) is a sequence of any four symbols chosen from the 26 letters in the alphabet and the ten digits. If all PINs are equally likely, what is the probability that a randomly chosen PIN contains a repeated symbol?
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to ______.
A bag contains 20 tickets numbered 1 to 20. Two tickets are drawn at random. The probability that both the numbers on the ticket are prime is ______.
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is ______.
