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If it rains on a given day the probability that it will rain the next day is 0.65 - OCR - GCSE Maths - Question 16 - 2023 - Paper 4
Question 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 ... show full transcript
Worked Solution & Example Answer:If it rains on a given day the probability that it will rain the next day is 0.65 - OCR - GCSE Maths - Question 16 - 2023 - Paper 4
Step 1
Complete the tree diagram
Answer
To complete the tree diagram, we first note the probabilities involved.
For Tuesday:
- Since it rained on Monday, we know the probabilities for Tuesday.
- Probability of Rain on Tuesday (given it rained on Monday): 0.65
- Probability of No Rain on Tuesday: 1 - 0.65 = 0.35
For Wednesday: 2. We have two branches based on whether it rained on Tuesday or not.
- If it rained on Tuesday:
- Probability of Rain on Wednesday: 0.65
- Probability of No Rain on Wednesday: 0.35
- If it did not rain on Tuesday:
- Probability of Rain on Wednesday: 0.3
- Probability of No Rain on Wednesday: 0.7
Thus, the completed tree diagram should display these probabilities.
Step 2
Find the probability that it rains on Wednesday.
Answer
To find the probability that it rains on Wednesday, we can use the law of total probability:
egin{align*} P(Rain ext{ on Wednesday}) & = P(Rain ext{ on Tuesday}) imes P(Rain ext{ on Wednesday | Rain on Tuesday}) \ & + P(No Rain ext{ on Tuesday}) imes P(Rain ext{ on Wednesday | No Rain on Tuesday}) \ & = (0.65 imes 0.65) + (0.35 imes 0.3) \ & = 0.4225 + 0.105 \ & = 0.5275. ext{Therefore, the probability that it rains on Wednesday is } 0.5275. \end{align*}