Probability that a leap year selected at random will contains 53 sunday is

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Solution

The correct option is D

27

Explanation for the correct option

We know that a leap year has 366days.

We have 52 weeks and 2 days. So, a leap year has 52Sundays.

The remaining 2days can be,

(Sunday, Monday),(Monday, Tuesday),(Tuesday, Wednesday),(Wednesday, Thursday),(Thursday, Friday),(Friday, Saturday),(Saturday, Sunday)

We have 7possibilities, from these possibilities we have two Sundays in it.

So, the required probability is 27

Hence, option(D) is the correct answer i.e. 27

`(7)/(366)``(28)/(183)``(1)/(7)``(2)/(7)`

Answer : D

Solution : A leap year has 366 days in which 52 and 2 days are extra. i.e. (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thrusdar), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday). So, probability that a leap year contains 53 Sunday = 2/7.

Answer : ` 2/7`

Solution : A leap year has 366 days=52 weeks and 2 days. <br> Now, 52 weeks contain 52 Sundays. <br> The remaining 2 days can be: <br> (i) Sunday and Monday (ii) Monday and Tuesday <br> (iii) Tuesday and Wednesday (iv) Wednesday and Thursday <br> (v) Thursday and Sunday (vi) Friday and Saturday <br> (vii) Saturday and Sunday <br> Out of these 7 cases, their are 2 cases favouring it to be Sunday. <br> ` :. ` P( a leap year having 53 Sundays ) =` 2/7`.

A leap year has 366 days with 52 weeks and 2 days.

Now, 52 weeks conatins 52 sundays.

The remaining two days can be:

1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday

Out of these 7 cases, there are two cases favouring it to be Sunday.

∴ P(a leap year having 53 Sundays) = `("Number of favourable outcomes")/"Number of all possible outcomes"`

`= 2/7`

Thus, the probability that a leap year selected at random will contain 53 Sundays is `2/7`.

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that

A non leap year has 365 days

There are 52 weeks and 1 day in 365 days

Number of sundays in 52 weeks = 52

So the one remaining day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday

Out of 7 days, we can have any of these days

The favourable outcome is 1 out of these 7 outcomes

Probability of getting 53 sundays in a non leap year = 1/7

Therefore, the probability that a non leap year selected at random will contain 53 sundays is 1/7.

✦ Try This: The probability that a leap year selected at random will contain 53 sundays is a. 7/366, b. 28/183, c. 1/7, d. 2/7

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.1 Problem 19

The probability that a non leap year selected at random will contain 53 sundays is a. 1/7, b. 2/7, c. 3/7, d. 5/7

Summary:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The probability that a non leap year selected at random will contain 53 sundays is 1/7

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Answer

Verified

Hint: There are $366$ days in leap year means $52$ weeks and $2$ extra days. Make the possibilities for two extra days and evaluate the probability.
Probability of any event A is defined as the ratio of the favourable outcomes to the total outcomes. The formula for the probability of A will be:
\[P(A) = \dfrac{{Favourable\,Outcomes}}{{Total\,Outcomes}}\]

Complete step-by-step answer:
We have given a leap year.
We have to evaluate the probability that a leap year has $53$ Sundays.
The difference between the leap and normal year is that the number of days in normal year is $365$ and the number of days in leap year is $366$
Therefore, in the leap year there are $52$ weeks and $2$ extra days. It means $52$ Sundays are included.
We have to make the conditions for $2$ extra days and our favourable outcomes will consist of $1$ Sunday so that total Sundays will be $53$.
The possibilities for two extra days will be:
{Monday, Tuesday}, {Tuesday, Wednesday}, {Wednesday, Thursday}, {Thursday, Friday}, {Friday, Saturday}, {Saturday, Sunday} and {Sunday, Monday}
In two of the cases {Saturday, Sunday} and {Sunday, Monday}, Sunday is present, therefore favourable outcomes will be $2$ and total possibilities are $7$, therefore, total outcomes will be $7$.
We know that probability of any event A is defined as the ratio of the favourable outcomes to the total outcomes. The formula for the probability of A will be:
\[P(A) = \dfrac{{Favourable\,Outcomes}}{{Total\,Outcomes}}\]
Therefore, the probability of $53$ Sundays in a leap year is $\dfrac{2}{7}$.

So, the correct answer is “Option B”.

Note: In these types of questions the total outcomes will not be equal to the total number of days because in $365$ days, the number of Sundays are fixed. Therefore, the total outcomes will come from $2$ extra days.