The probability that it rains on Monday \(\frac{3}{5}\)
If it rains on Monday, the probability that it rains on Tuesday is \(\frac{4}{7}\)
If it does not rain on Monday, the probability that it rains on Tuesday is \(\frac{5}{7}\)
(a) Complete the tree diagram.
(b) Find the probability that it rains
(i) on both days,
(ii) on Monday but not on Tuesday,
(iii) on only one of the two days.
(c) If it does not rain on Monday and it does not rain on Tuesday, the probability that it does not rain on Wednesday is \(\frac{1}{4}\)
Calculate the probability that it rains on at least one of the three days.
(a)
(b)(i) Ans: \(\frac{12}{35}\)
Multiply the probability of rain on Monday (\(\frac{3}{5}\)) by the probability of rain on Tuesday given rain on Monday (\(\frac{4}{7}\)).
(b)(ii) Ans: \(\frac{9}{35}\)
Multiply the probability of rain on Monday (\(\frac{3}{5}\)) by the probability of no rain on Tuesday given rain on Monday (\(\frac{3}{7}\)).
(b)(iii) Ans: \(\frac{19}{35}\)
Add the probability of rain only on Monday (\(\frac{9}{35}\)) and rain only on Tuesday (\(\frac{2}{5} \times \frac{5}{7} = \frac{10}{35}\)).
(c) Ans: \(\frac{34}{35}\)
First, find the probability of no rain on all three days (\(\frac{2}{5} \times \frac{2}{7} \times \frac{1}{4} = \frac{1}{35}\)). Subtract this from 1 to get the probability of rain on at least one day.
