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Romelu picks a shirt and shorts - OCR - GCSE Maths - Question 24 - 2018 - Paper 1
Question 24
Romelu picks a shirt and shorts. The probability he picks a red shirt is 0.4. The probability he picks white shorts is 0.7. (a) Complete the tree diagram. Shirt ... show full transcript
Worked Solution & Example Answer:Romelu picks a shirt and shorts - OCR - GCSE Maths - Question 24 - 2018 - Paper 1
Step 1
Complete the tree diagram.
Answer
In order to complete the tree diagram, we need to fill in the missing probabilities. The probability of picking a red shirt is given as 0.4, which means the probability of not picking a red shirt is:
Next, we handle the shorts. The probability of picking white shorts is given as 0.7, meaning the probability of not picking white shorts is:
Putting this information into the tree diagram, we get:
Shirt ├─ Red │ └─ 0.4 └─ Not red └─ 0.6
Shorts ├─ White │ └─ 0.7 └─ Not white └─ 0.3
Step 2
Calculate the probability that Romelu picks a red shirt but does not pick white shorts.
Answer
To find the probability that Romelu picks a red shirt but does not pick white shorts, we multiply the probabilities of these independent events. From the tree diagram:
- Probability of picking a red shirt:
- Probability of not picking white shorts:
Thus, the combined probability is:
Therefore, the probability that Romelu picks a red shirt but does not pick white shorts is 0.12.