The probability that in a year of the 22^{nd} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) century consists of $100$ years. In any century,there are $25$ leap years and $75$ non-leap years.Probability of choosing a leap year $P(L) = \fra

Vedclass · Accepted Answer

$\frac{5}{28}$

Vedclass · Answer

(D) century consists of $100$ years. In any century,there are $25$ leap years and $75$ non-leap years.Probability of choosing a leap year $P(L) = \frac{25}{100} = \frac{1}{4}$.Probability of choosing a non-leap year $P(NL) = \frac{75}{100} = \frac{3}{4}$.$A$ leap year has $366$ days,which is $52$ weeks and $2$ extra days. The probability of having $53$ Sundays in a leap year is $\frac{2}{7}$.$A$ non-leap year has $365$ days,which is $52$ weeks and $1$ extra day. The probability of having $53$ Sundays in a non-leap year is $\frac{1}{7}$.Total probability $= P(L) 	imes P(53 	ext{ Sundays in leap year}) + P(NL) 	imes P(53 	ext{ Sundays in non-leap year})$.Total probability $= (\frac{1}{4} 	imes \frac{2}{7}) + (\frac{3}{4} 	imes \frac{1}{7}) = \frac{2}{28} + \frac{3}{28} = \frac{5}{28}$.

The probability that in a year of the $22^{nd}$ century chosen at random there will be $53$ Sundays is

Similar Questions

$A$ fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

$A$ box contains $25$ tickets numbered $1, 2, \dots, 25$. If two tickets are drawn at random,then the probability that the product of their numbers is even is:

If $E$ and $F$ are events with $P(E) \le P(F)$ and $P(E \cap F) > 0,$ then

$A$ bag contains $7$ black and $5$ white balls. $A$ ball is drawn out and replaced in the bag. Then a ball is drawn again. What is the probability that the first ball was white and the second black?

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (the first card is not replaced before drawing the second card).

Vedclass Test Series

Exam Paper Generator

Online Exam Module