Question

find probability of that month June have 5 mondays in a leap year.

Answer 1

Number of days in the month of Junein a leap or non-leap year = 31
There are four complete weeks in the month of June.
There are three more extra days in the month.
If the month starts on Saturday or Sunday or Monday, there are 5 Mondays in the month of June.
So, the probability of getting 5 Mondays in the month of June(or any month with 31 days) = 3/7

Answer 2

The probability of that month June have 5 mondays in a leap year is 2/7

Given :

The month of June in a leap year

To find :

The probability of that month June have 5 mondays in a leap year

Solution :

Step 1 of 3 :

Find total number of possible outcomes

The month of June has 30 days

30 days = 4 weeks 2 days

Now 4 weeks contains 4 Mondays

2 days is one of the below

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

So the total number of possible outcomes = 7

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that month June have 5 mondays in a leap year.

So the total event points for the event A is ( Sunday, Monday), ( Monday, Tuesday)

So the total number of possible outcomes for the event A is 2

Step 3 of 3 :

Find the probability

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{2}{7} }$

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