# tree diagram

#### SpringFan25

thats right

• andyboy179

#### andyboy179

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??

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.

• andyboy179

#### andyboy179

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?

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