find the probability that a leap year chosen at random has ( 1 ) 52 Sunday ( 2 ) 53 Sunday
Answers
Answer:
5/7, 2/7
Step-by-step explanation:
1. In a leap year there are 366 days.
We have,
366 days = 52 weeks and 2 days
Thus, a leap year has always 52 Sundays.
The remaining 2 days can be:
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday.
Clearly, there are seven elementary events associated with this random experiment,
Let A be the event that a leap year has 52 Sundays.
Clearly, the event A will happen if the last two days of the leap year are not Sunday and Monday or Saturday and Sunday.
∴ Favorable number of elementary events = 5
Hence, required probability = 5/7
2. In a leap year there are 366 days.
We have,
366 days = 52 weeks and 2 days
Thus, a leap year has always 52 Sundays.
The remaining 2 days can be:
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday.
Clearly, there are seven elementary events associated with this random experiment,
Let A be the event that a leap year has 53 Sundays.
Clearly, the event A will happen if the last two days of the leap year are either Sunday and Monday or Saturday and Sunday.
∴ Favorable number of elementary events = 2
Hence, required probability = 2/7
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