Question

Medal!
The chart shows the membership in the High School Band. What is the probability that a boy and a girl chosen randomly will both be seniors?

HS Band Freshman Sophmores juniors seniors
Boys 10 7 10 9
Girls 8 11 9 7


A. 1/4
B. 1/5
C. 1/9
D. 1/20

Answer 1

i got B as my answer

Answer 2

I wonder if the order of selection matters. That is, BG and then GB. Somehow, I don't think so.

@Yttrium What do you think?

Answer 3

What I know is that it is all about total probability theorem.

Answer 4

P(SB) = 9/36; P(SG) = 7/35

P(SB and SG) = (9/36)*(7/35) = ?

Answer 5

Order doesn't appear to matter - you know you're choosing from the boys, then you know you're choosing from the girls

HS Band Freshman Sophmores juniors seniors
Boys 10 7 10 9 total boys = 36
Girls 8 11 9 7 total girls = 35

senior boy = 9/36 = 1/4
senior girl = 7/35 = 1/5

multiply those two.

Answer 6

multiply which two?

Answer 7

oh i see now.

Answer 8

the only two that are there... the same two directrix has

Answer 9

1/20

Answer 10

@kropot72 Please tell us what you think.

Answer 11

is 1/20 the right answer guys?

Answer 12

@Directrix it's essentially conditional. "boy and a girl chosen randomly" = Given you pick a boy, given you pick a girl. You're choosing a boy from the group of boys, you're not choosing from the entire group. Same for the girl.

Answer 13

It doesn't mean the same as "what is the probability you pick a boy and a girl and both are seniors"

Answer 14

But probability problems often have these annoying wording issues...

Answer 15

The events 'choose a boy' and 'choose a girl' are independent. Therefore the required probability is P(pick a senior girl) * P(pick a senior boy) = (9/36) * (7/35) = 1/20