Advertisements
Advertisements
प्रश्न
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
उत्तर
When a coin is tossed, the possible outcomes are head (H) and tail (T).
If a coin is tossed twice, the possible outcomes are given by
S = {HH, HT, TH, TT}
Again, if the second draw results in a head, then a dice is rolled. The events associated with this experiment is given by
A = {(HH, 1), (HH, 2), (HH, 3), (HH, 4), (HH, 5), (HH, 6), (TH, 1), (TH, 2), (TH, 3), (TH, 4), (TH, 5), (TH, 6)}
Hence, the sample space for this experiment is given by
(S ∪ A) = {(HH, 1), (HH, 2), (HH, 3), (HH, 4), (HH, 5), (HH, 6),
(TH, 1),
(TH, 2), (TH, 3), (TH, 4), (TH, 5), (TH, 6), (HT), (TT)}
APPEARS IN
संबंधित प्रश्न
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 recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?
A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find 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 twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.
A coin is tossed repeatedly until a tail comes up for the first time. 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?
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.
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.
A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
A die is thrown repeatedly until a six comes up. What is 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.
(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 neither an ace nor 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 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
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?
The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.
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?
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?
Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.
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.
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}
Compute P(A), P(B) and P(A ∩ B).
n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.
What is the probability that the 13th days of a randomly chosen month is Friday?
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).
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
Six boys and six girls sit in a row randomly. The probability that all girls sit together is
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is
How many two-digit positive integers are multiples of 3?
What is the probability that a randomly chosen two-digit positive integer is a multiple 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 ______.
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 ______.
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 ______.
