What are the chances...(probability of random calendar-month shuffle)?

Question

"If the twelve months of the calendar were randomly "shuffled", what is the probability that the first three months "dealt" would each have thirty-one days in them?"

7/12 x 6/11 x 5/10 .....Right? or no?

And also please, what is the decimal and/or percentage answer to this question?

Thanks!!!

Answer 1

Exactly right! Since there are 7 months with 31 days, the probability of the first card being a 31-day month is 7/12. Subsequent draws are 6/11 and 5/10.

7 .... 6 .... 5
--- x --- x ----
12 . 11 . 10

To calculate this fraction, I'd cancel some terms in your numerator and denominator:

7 .... 1 .... 1
--- x --- x ----
2 ... 11 ... 2

Now just multiply across:

Probability is 7/44

Using a calculator this is approximately:
0.1590909...
or 15.90909%

Answer 2

There are 12 months.
7 months have 31 days.
5 months have less than 31 days.
(7/12)(6/11)(5/10) correct.
7 x 6 x 5 / 12 x 11 x 10 =210/1320=0.159 or 15.9 %

Answer 3

Yes, your reasoning is correct. Once you multiply this out, getting the decimal is as simple as converting the fraction to decimal (divide the numerator by the denominator), and the percentage can be easily found from that.

Answer 4

You are right now multiply them to get your answer in a decimal.

(210)/1320 = 7/44 = 0.159 = 15.9%