Advertisements
Advertisements
प्रश्न
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.
उत्तर
Out of 16 balls, two balls can be drawn in 16C2 ways.
∴ Total number of elementary events = 16C2 = 120
'Two balls drawn are of the same colour' means that both are either white or black or red.
Out of seven white balls, two white balls can be drawn in 7C2 ways.
Similarly, two black balls can be drawn from five black balls in 5C2 ways and two red balls can be drawn from four red balls in 4C2 ways.
Therefore, number of ways of drawing two balls of the same colour = 7C2 + 5C2 + 4C2 = 21 + 10 + 6 = 37
i.e. favourable number of ways = 37
Hence, required probability = \[\frac{37}{120}\]
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 four times.
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.
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.
If a coin is tossed three times (or three coins are tossed together), then describe 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 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 coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment.
There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is either a black card or a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is spade or an ace
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is 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 and two are white
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:
(i) just one ace
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?
There are four men and six women on the city councils. If one council member is selected for a committee at random, how likely is that it is a women?
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.
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.
An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.
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}
List the composition of the event A ∪ B, and calculate P(A ∪ B) by addting the probabilities of elementary events.
n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
What is the probability that a leap year will have 53 Fridays or 53 Saturdays?
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 E and E2 are independent evens, write the value of P \[\left( ( E_1 \cup E_2 ) \cap (E \cap E_2 ) \right)\]
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
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 sample space of the experiment?
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?
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 ______.
If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls 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 ______.
