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One weekend the Keddie family is going to do a sports quiz and a music quiz - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3
Question 6
One weekend the Keddie family is going to do a sports quiz and a music quiz. The probability that the family will win the sports quiz is 0.3. The probability that t... show full transcript
Worked Solution & Example Answer:One weekend the Keddie family is going to do a sports quiz and a music quiz - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 3
Step 1
Complete the probability tree diagram.
Answer
To complete the probability tree diagram, we first note the probabilities provided:
- Sports quiz: Probability of winning = 0.3; Probability of not winning = 0.7 (since 1 - 0.3 = 0.7).
- Music quiz: Probability of winning = 0.35; Probability of not winning = 0.65 (since 1 - 0.35 = 0.65).
Thus, the complete tree diagram is as follows:
Sports quiz
├─ Win (0.3)
│ ├─ Music quiz Win (0.35)
│ └─ Music quiz Do not win (0.65)
└─ Do not win (0.7)
├─ Music quiz Win (0.35)
└─ Music quiz Do not win (0.65)
Step 2
Work out the probability that the Keddie family will win both the sports quiz and the music quiz.
Answer
The probability that the Keddie family will win both quizzes can be found by multiplying the probabilities of winning each quiz:
- Probability of winning the sports quiz = 0.3.
- Probability of winning the music quiz = 0.35.
Therefore, the combined probability is:
Hence, the probability that the Keddie family will win both the sports quiz and the music quiz is 0.105.