Advertisements
Advertisements
प्रश्न
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
पर्याय
47/66
10/33
1/3
1
उत्तर
47/66
Out of 12 balls, two balls can be drawn in 12C2 ways.
∴ Total number of elementary events, n(S) = 12C2 = 66
We observe that at least one ball of each colour can be drawn in one of the following mutually exclusive ways:
(i) 1 red and 1 white
(ii) 1 red and 1 blue
(iii) 1 white and 1 blue
Thus, if we define three events A, B and C as follows:
A = drawing 1 red and 1 white
B = drawing 1 red and 1 blue
C = drawing 1 white and 1 blue
then, A, B and C are mutually exclusive events.
∴ Required probability = P(A ∪ B ∪ C)
= P(A) + P(B) + P(C)
=\[\frac{^{3}{}{C}_1 \times ^{4}{}{C}_1}{^{12}{}{C}_2} + \frac{^{3}{}{C}_1 \times ^{5}{}{C}_1}{^{12}{}{C}_2} + \frac{^{4}{}{C}_1 \times ^{5}{}{C}_1}{^{12}{}{C}_2}\]
= \[\frac{3 \times 4}{66} + \frac{3 \times 5}{66} + \frac{4 \times 5}{66}\]
= \[\frac{12}{66} + \frac{15}{66} + \frac{20}{56} = \frac{47}{66}\]
APPEARS IN
संबंधित प्रश्न
Describe the sample space for the indicated experiment: A coin is tossed four times.
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
What is the total number of elementary events associated to the random experiment of throwing three dice together?
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.
A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for 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.
List all events associated with the random experiment of tossing of two coins. How many of them 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 a diamond card
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black card
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 two are blue and one is red
The letters of the word' CLIFTON' are placed at random in a row. What is the chance that two vowels come together?
Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together.
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 6?
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 boys?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has 1 boys and 2 girls?
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?
An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that one ball is white.
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Using the addition law of probability, find P(A ∪ B).
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
The probability of getting a total of 10 in a single throw of two dices 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
The probabilities of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither Anor B happens is
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
How many two-digit positive integers are multiples of 3?
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 ______.
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is ______.
