Question

In a class of 30 students , 20 of them are boys .
If two students are chosen at random,
what is the probability they are different genders
and are born on the same day of the year

Answer 1

Take Probabalilty conception in use.

Answer 2

P( two students have different gender & born on same day of year)
= P( (BG or GB) & born same day of year)

Answer 3

BG = choosing a boy , then choosing a girl

Answer 4

P( (BG or GB) & born same day of year)
= P( BG or GB) * P ( two students born same day of year) ?

Answer 5

= ( 2*20/30 * 10/29) ( 1/365) ?

Answer 6

it seems to me that they are independent

Answer 7

gender does seem independent of birthdate

Answer 8

did i do this wrong?

Answer 9

I don't think so. But I'm not the best person to consult when statistics and probability is concerned... you'd best get a second opinion (or a third, if I'm the second)

Answer 10

with general multiplication rule we have
P( BG or GB) * P ( two students born same day of year | BG or GB)

Answer 11

Whether a boy is chosen first or a girl is chosen first the probability of different genders being chosen is
\[P(different\ genders)=\frac{20\times 10}{30\times 29}\]
The required probability is
\[\frac{20\times 10}{30\times 29\times365}\]

Answer 12

but I got BG or GB

Answer 13

so should be times 2

Answer 14

you can pick a boy first, then girl, or you can pick a girl first then boy

Answer 15

My bad. You are correct. There are two ways of choosing different genders, each way with the same probability. The probability of choosing a boy first is 20/30. The probability of choosing a girl next is 10/29.
The probability of choosing a girl first is 10/30. The probability of choosing a boy next is 20/29.
\[\frac{20\times 10}{30\times 29}=\frac{10\times 20}{30\times 29}\]