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What is the chance that a leap year selected at random will contain 53 sunday ?

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Answer 1 · 2017-11-15T17:06:13

$2/7.$

A leap year has $366$ days, so it contains $52$ weeks

and $2$ days.

$[because, 366" days="52" weeks"xx7" days"+2" days.]"$

Now, these $52$ weeks contain $52$ Sundays, so the

$53^(rd)$ Sunday must happen from $2$ days.

These $2$ days can be,

(1) : Sunday, Monday;

(2) : Monday, Tuesday;

(3) : Tuesday, Wednesday;

(4) : Wednesday, Thursday;

(5) : Thursday, Friday:

(6) : Friday, Saturday; and

(7) : Saturday, Sunday.

Thus, out of $7$ possibilities enumerated above, $53^(rd)$ Sunday

can happen in $2$ ways, [i.e., alternative (1) and (7)].

Hence, the Reqd. Prob. $=2/7.$