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Romelu picks a shirt and shorts - OCR - GCSE Maths - Question 24 - 2018 - Paper 1

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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.

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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:

10.4=0.61 - 0.4 = 0.6

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:

10.7=0.31 - 0.7 = 0.3

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.

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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: P(Red)=0.4P(Red) = 0.4
  • Probability of not picking white shorts: P(NotWhite)=0.3P(Not \, White) = 0.3

Thus, the combined probability is:

P(RedandNotWhite)=P(Red)imesP(NotWhite)=0.4imes0.3=0.12P(Red \, and \, Not \, White) = P(Red) imes P(Not \, White) = 0.4 imes 0.3 = 0.12

Therefore, the probability that Romelu picks a red shirt but does not pick white shorts is 0.12.

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