Question

find the probability that a non leap year should have only 52 Sundays​

Answer 1

6/7 or 0.86

Step-by-step explanation:

Direct Method :

step 1. Possible outcomes for 1 odd day

The odd day may be either Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday. Therefore, the total number of possible outcomes or elements of a sample space is 7.

step 2. Probability of 1 Odd day not to be Sunday

The sample space S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}

Expected events of A = {Mon, Tue, Wed, Thu, Fri, Sat}

P(A) ={Mon, Tue, Wed, Thu, Fri, Sat}÷{Sun, Mon, Tue, Wed, Thu, Fri, Sat}

P(A) = 6/7

P(A) = 0.86

6/7 or 0.86 is probability for 52 Sundays in a non-leap year.

Complement Method :

step 1. Possible outcomes for 1 odd day

The odd day may be either Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday. Therefore, the total number of possible outcomes or elements of a sample space is 7.

step 2. Probability of 1 Odd day to be Sunday

The sample space S = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Expected event of A = {Sunday}

P(A) = {Sunday}/{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

P(A) = 1/7

P(A) = 0.14

step 3 Finding the complement of event A for one odd day not to be Sunday

= 1 - P(A)

= 1 - 0.14

P(A’) = 0.86

0.86 is probability for 52 Sundays in a non-leap year.