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 and then a die is rolled only in case a head is shown on the coin.
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?
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.
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.
A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.
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 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?
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 die is thrown repeatedly until a six comes up. What is 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.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king
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 a jack, queen or a king
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 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
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
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?
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?
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?
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 both the balls are red .
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).
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).
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.
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
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.
Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
Six boys and six girls sit in a row randomly. The probability that all girls sit together is
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
What is the probability that a randomly chosen two-digit positive integer is a multiple of 3?
A typical PIN (personal identification number) is a sequence of any four symbols chosen from the 26 letters in the alphabet and the ten digits. If all PINs are equally likely, what is the probability that a randomly chosen PIN contains a repeated symbol?
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
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 ______.
