SE 2020)
49. Find the probability that a leap year selected at random will contain
53 Sundays and 53 Mondays.
(CBSE 2020]
Answers
Answer:
Total number of days in a leap year is 366.
It will contain 52 weeks and 2 days.
These two days can be
S={(Sun,Mon);(Mon,Tues);(Tues,Wed);(Wed,Thurs);(Thurs,Fri);(Fri,Sat);(Sat,Sun)}
Therefore n(S)=7
Let A be the event of getting 53 sundays.
Therefore A={(Sun,Mon);(Sat,Sun)}
For 53 Sundays , probability is P(A)=
7
2
Let B be the event of getting 53 mondays.
Therefore B={(Sun,Mon);(Mon,Tues)}
For 53 Mondays , probability is P(B)=
7
2
=27
This includes one ways where sunday and monday simultaneously Occur
(i.e) A∩B={Sun,Mon}
Probability for this is P(A∩B)=
7
1
.
=17
Hence required probability that a leap year selected at random contain 53 sundays or 53 mondays is
P(A∪B)=P(A)+P(B)−P(A∩B)
=
7
2
+
7
2
−
7
1
=
7
2+2−1
Therefore the required probability is
7
3
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