The probability that year 2016 to have 53 Mondays isA) 1/7B) 2/7C) 5/7

1.	The probability that year 2016 to have 53 Mondays isA) 1/7B) 2/7C) 5/7D) 6/7
Answer» Correct option is: B) \(\frac 27\) 2016 is a leap year in which total number of days is 366. \(\because\) \(\frac {366}7 = 52 + \frac 27\) \(\therefore\) Year 2016 definitely have 52 Mondays and there are two extra days left which may be (i) Monday & Tuesday, (ii) Tuesday & Wednesday (iii) Wednesday & Thursday (iv) Thursday & Friday (v) Friday & Saturday (vi) Saturday & Sunday (vii) Sunday & Monday. For 53 Mondays there are two possibilities, left 2 days may be Sunday & Monday or Monday & Tuesday. \(\therefore\) Total favourable outcomes which favours 53 Mondays = 2 Total possible outcomes = 7. \(\therefore\) Probability that year 2016 to have 53 Mondays = \(\frac {Total \, favourable \, outcome}{Total \, No.\, of \,outcomes}\) = \(\frac 27\) Hence, the probability that year 2016 to have 53 Mondays is \(\frac 27\) Correct option is: B) \(\frac{2}{7}\)

The probability that year 2016 to have 53 Mondays isA) 1/7B) 2/7C) 5/7D) 6/7

Answer»

Correct option is: B) \(\frac 27\)

2016 is a leap year in which total number of days is 366.

\(\because\) \(\frac {366}7 = 52 + \frac 27\)

\(\therefore\) Year 2016 definitely have 52 Mondays

and there are two extra days left which may be

(i) Monday & Tuesday, (ii) Tuesday & Wednesday (iii) Wednesday & Thursday (iv) Thursday & Friday (v) Friday & Saturday (vi) Saturday & Sunday (vii) Sunday & Monday.

For 53 Mondays there are two possibilities, left 2 days may be Sunday & Monday or Monday & Tuesday.

\(\therefore\) Total favourable outcomes which favours 53 Mondays = 2

Total possible outcomes = 7.

\(\therefore\) Probability that year 2016 to have 53 Mondays

= \(\frac {Total \, favourable \, outcome}{Total \, No.\, of \,outcomes}\) = \(\frac 27\)

Hence, the probability that year 2016 to have 53 Mondays is \(\frac 27\)

Correct option is: B) \(\frac{2}{7}\)

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