Find the probability that 5 Sundays occur in the month of November of

1.	Find the probability that 5 Sundays occur in the month of November of a randomly selected year.
Answer» In month of November 4 sundays are fixed. But there are two extra days. They may be {(Sun, Mon), (Mon, Tues), (Tues, Wed), (Wed, Thurs), (Thurs, Fri), (Fri, Sat), (Sat, Sun)} Number of favourable outcomes = 2 Required probability (5 sundays) = \(\frac{2}{7}\) In any randomly selected year, the Month of November will have 30 days. Now out of these 30 days, we will have 4 complete weeks (i.e. 28 days) having 4 Sundays. For the remaining two days, we have the following possibilities: (i) Saturday and Sunday, (ii) Sunday and Monday, (iii) Monday and Tuesday, (iv) Tuesday and Wednesday, (v) Wednesday and Thursday, (vi) Thursday and Friday, (vii) Friday and Saturday. Thus, the possibility of having a 5th Sunday = \(\frac{2}{7}\).

Find the probability that 5 Sundays occur in the month of November of a randomly selected year.

Answer»

In month of November 4 sundays are fixed.

But there are two extra days. They may be {(Sun, Mon), (Mon, Tues), (Tues, Wed), (Wed, Thurs), (Thurs, Fri), (Fri, Sat), (Sat, Sun)}

Number of favourable outcomes = 2

Required probability (5 sundays) = \(\frac{2}{7}\)

In any randomly selected year, the Month of November will have 30 days.
Now out of these 30 days, we will have 4 complete weeks (i.e. 28 days) having 4 Sundays.
For the remaining two days, we have the following possibilities:
(i) Saturday and Sunday,
(ii) Sunday and Monday,
(iii) Monday and Tuesday,
(iv) Tuesday and Wednesday,
(v) Wednesday and Thursday,
(vi) Thursday and Friday,
(vii) Friday and Saturday.
Thus, the possibility of having a 5th Sunday = \(\frac{2}{7}\).

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