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.