Advertisements
Advertisements
प्रश्न
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has all girls?
उत्तर
Total number of students = (10 + 8) = 18
Let S be the sample space.
Then n(S) = number of ways of selecting 3 students out of 18 = 18C3 ways
Out of eight girls, three girls can be selected in 8C3 ways.
∴ Favourable number of events, n(E) = 8C3
Hence, required probability =\[\frac{^{8}{}{C}_3}{^{18}{}{C}_3} = \frac{8 \times 7 \times 6}{18 \times 17 \times 16} = \frac{7}{102}\]
APPEARS IN
संबंधित प्रश्न
Describe the sample space for the indicated experiment: A coin is tossed three times.
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?
An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
Write the sample space for the experiment of tossing a coin four times.
What is the total number of elementary events associated to the random experiment of throwing three dice together?
A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; if it shows head, we throw a die. Find the sample space of this experiment.
A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?
An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
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 drawn at random from a pack of 52 cards. Find the probability that the card drawn is black and a king
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 diamond card
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not an ace
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 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are white
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are of the same colour.
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that two are blue and one is red
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have two men?
Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.
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 not a multiple of 4?
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 divisible by 5?
n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
If E and E2 are independent evens, write the value of P \[\left( ( E_1 \cup E_2 ) \cap (E \cap E_2 ) \right)\]
Two dice are thrown simultaneously. The probability of obtaining total score of seven is
A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is
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
Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds and hearts and black suits are clubs and spades. The cards J, Q, and K are called face cards. Suppose we pick one card from the deck at random. What is the event that the chosen card is a black face card?
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?
Two boxes are containing 20 balls each and each ball is either black or white. The total number of black ball in the two boxes is different from the total number of white balls. One ball is drawn at random from each box and the probability that both are white is 0.21 and the probability that both are black is k, then `(100"k")/13` is equal to ______.
