tree diagram

Oct 2008
897
3
Bristol, England
hi, this is my question:

past records show that in a typica week in september it rains on 4 days out of 7.
A) Copy the tree diagram and fill in the proibabilities for the first and second saturdays in sepember. (tree diagram below) ( WR= will rain, WNR= will not rain)

View attachment 17044


have i filled it in correct? if not where am i going wrong.

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Oct 2008
897
3
Bristol, England
Thanks!
the next question says:
C) Calculate the probability that it rains on at least one of the saturdays.

so would i do, 4/7 x 4/7 x 4/7= 64/343??
 
Dec 2009
3,120
1,342
Thanks!
the next question says:
C) Calculate the probability that it rains on at least one of the saturdays.

so would i do, 4/7 x 4/7 x 4/7= 64/343??
No!

Referring to the tree diagram.....
It will rain on at least one Saturday if it rains on the first Saturday and doesn't on the second,
or..... it doesn't rain on the first Saturday and it rains on the second,
or....it rains on both Saturdays.

That's 3 options.

The probabilities you've written indicate that there is a 4/7 chance it'll rain on a Saturday.

Hence the successful outcomes (rains on at least one Saturday) are...

R.........WNR
WNR....R
R.........R

In each of these cases we multiply the probabilities at each stage

R NR means it rains the first Saturday and doesn't rain on the second Saturday.

From your tree diagram, multiply those probabilities

\(\displaystyle \frac{4}{7}\ \frac{3}{7}=\frac{4(3)}{7(7)}=\frac{12}{49}\)

That probability corresponds to one of the four final branches.

There are 2 more.

Independently calculate those probabilities as above and then sum all 3 answers for the 3 branches.
 
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Oct 2008
897
3
Bristol, England
okay.
so would i do 4/7 x 4/7= 16/49
4/7 x 3/7= 12/49
3/7 x 4/7= 12/49
then, 16/49 + 12/49 + 12/49= 40/49?
 
Dec 2009
3,120
1,342
okay.
so would i do 4/7 x 4/7= 16/49 =probability of rain on both Saturdays
4/7 x 3/7= 12/49 =probability of rain on 1st Saturday and a dry 2nd Saturday
3/7 x 4/7= 12/49 =probability of a dry 1st Saturday and a wet 2nd Saturday
then, 16/49 + 12/49 + 12/49= 40/49?
That's exactly it yes, corresponding to the appropriate 3 arms of the tree diagram.
 
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