16 If it rains on a given day the probability that it will rain the next day is 0.65. If it does not rain on a given day the probability that it will rain the next day is 0.3. It rained on Monday.
(a) Complete the tree diagram.[2]
(b) Find the probability that it rains on Wednesday. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Tuesday [0].65 oe and [0].35 oe in the correct places and Wednesday [0].65 oe with [0].35 oe and [0].3 oe with [0].7 oe in the correct places
2
B1 for one pair of probabilities correct in one branch e.g Tuesday or one of the Wednesday branches
Mark scheme (b)
Answer
Marks
Part marks and guidance
[0].5275 or [0].528 or 0.53 or \(\frac{211}{400}\) oe nfww
3
M2 for [0].65 × [0].65 + [0].35 × [0].3 oe or M1 for [0].65 × [0].65 or [0].35 × [0].3 oe implied by .4225 or .105 or \(\frac{169}{400}\) or \(\frac{21}{200}\) oe
If (a) is not correct FTtheir tree for 3 marks,M2 and M1 Allow 52.75%, 52.8% 53% for 3 marks
