Advertisements
Advertisements
प्रश्न
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Advertisements
उत्तर
Probability of year being a leap year = `1/4`
Probability of year being non – leap year = `3/4`
A leap year has 366 days
`366/7` = 52 weeks + 2 days
In 52 weeks,
we get 52 Sundays.
From the remaining two days we should get one Sunday
The remaining two days can be any one of the following combinations.
Saturday and Sunday, Sunday and Monday, Monday and Tuesday, Tuesday and Wednes¬day, Wednesday and Thursday, Thursday and Friday, Friday and Saturday of the seven combinations two have Sundays.
∴ (Probability of getting a Sunday = `2/7`
Selecting a leap year = `1/4`
∴ In every four consecutive years we get one leap year
∴ Probability of getting 53 Sundays = `2/7 xx 1/4 xx 1/14`
APPEARS IN
संबंधित प्रश्न
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Determine P(E|F).
Two coins are tossed once, where
E: tail appears on one coin, F: one coin shows head
Determine P(E|F).
Two coins are tossed once, where
E: no tail appears, F: no head appears
Determine P(E|F).
Mother, father and son line up at random for a family picture
E: son on one end, F: father in middle
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are black
Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4
Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.
If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.
Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card being a king and second card not being a king is:
If for two events A and B, P(A – B) = `1/5` and P(A) = `3/5`, then `P(B/A)` is equal to ______.
If for any two events A and B, P(A) = `4/5` and P(A ∩ B) = `7/10`, then `P(B/A)` is equal to ______.
Which conditional probabilities are equal to 1 when \[P(F)\neq 0\]?
