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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
The probability that a leap year selected at random contains either $53$ Sundays or $53 $ Mondays, is
  • A
    $\frac{2}{7}$
  • B
    $\frac{4}{7}$
  • ✓
    $\frac{3}{7}$
  • D
    $\frac{1}{7}$
✓

Answer

Correct option: C.
$\frac{3}{7}$
c
(c) A leap year consists of $366$ days comprising of $52$ weeks and $2$ days.

There are $7$ possibilities for these $2$ extra days viz.

$(i)$ Sunday, Monday,                 $(ii)$ Monday, Tuesday,

$(iii)$ Tuesday, Wednesday,        $(iv)$ Wednesday, Thursday,

$(v)$ Thursday, Friday,                $(vi)$ Friday, Saturday and

$(vii)$ Saturday, Sunday.

Let us consider two events :

$A:$ the leap year contains $53$ Sundays

$B:$ the leap year contains $53$ Mondays.

Then we have $P(A) = \frac{2}{7},\,\,P(B) = \frac{2}{7},\,\,P(A \cap B) = \frac{1}{7}$

$\therefore $ Required probability $ = P(A \cup B)$

$ = P(A) + P(B) - P(A \cap B) = \frac{2}{7} + \frac{2}{7} - \frac{1}{7} = \frac{3}{7}.$

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