Advertisements
Advertisements
प्रश्न
What is the probability that a leap year will have 53 Fridays or 53 Saturdays?
उत्तर
We know that a leap year has 366 days (i.e. 7 \[\times\] 52 + 2) = 52 weeks and 2 extra days
The sample space for these two extra days are as follows:
S = {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
There are 7 cases.
i.e. n(S) = 7
Let E be the event that a leap year has 53 Fridays or 53 Saturdays.
Then E = { (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
i.e. n(E) = 3
\[\therefore P\left( E \right) = \frac{n\left( E \right)}{n\left( S \right)} = \frac{3}{7}\]
Hence, the probability that a leap year has 53 Fridays or 53 Saturdays is \[\frac{3}{7} .\]
APPEARS IN
संबंधित प्रश्न
Describe the sample space for the indicated experiment: A coin is tossed four times.
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.
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.
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?
The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe 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.
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.
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 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?
2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the sample space for the experiment in which a room is selected and then a person.
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.
A coin is tossed. Find the total number of elementary events and also the total number events associated with the random 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?
A card is picked up from a deck of 52 playing cards.
What is the event that the chosen card is a black faced card?
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 black and 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 a black card
Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least 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?
The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. what is the probability that they belong to different suits?
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 greater than 12?
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?
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 at least one girl?
Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.
An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
A die is rolled, then the probability that a number 1 or 6 may appear is
A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of them is an ace 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 ______.
