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Amanda has two fair 3-sided spinners - Edexcel - GCSE Maths - Question 6 - 2020 - Paper 3
Question 6
Amanda has two fair 3-sided spinners. Amanda spins each spinner once. (a) Complete the probability tree diagram. Spinner A lands on 2 Spinner B does not land o... show full transcript
Worked Solution & Example Answer:Amanda has two fair 3-sided spinners - Edexcel - GCSE Maths - Question 6 - 2020 - Paper 3
Step 1
Complete the probability tree diagram.
Answer
To complete the probability tree diagram, we need to identify the possible outcomes for both spinners.
For each spinner:
-
Spinner A:
- Probability of landing on 2 = ( \frac{1}{3} )
- Probability of not landing on 2 = ( \frac{2}{3} )
-
Spinner B:
- Probability of landing on 2 = ( \frac{1}{3} )
- Probability of not landing on 2 = ( \frac{2}{3} )
Thus, the completed diagram will have the following branches:
- Spinner A → lands on 2 (( \frac{1}{3} ))
- Spinner A → does not land on 2 (( \frac{2}{3} ))
Next, for each outcome of Spinner A, we further branch into Spinner B:
-
If Spinner A lands on 2:
- Spinner B → lands on 2 (( \frac{1}{3} ))
- Spinner B → does not land on 2 (( \frac{2}{3} ))
-
If Spinner A does not land on 2:
- Spinner B → lands on 2 (( \frac{1}{3} ))
- Spinner B → does not land on 2 (( \frac{2}{3} ))
These probabilities can now be used for part (b).
Step 2
Work out the probability that Spinner A lands on 2 and Spinner B does not land on 2.
Answer
To find the probability that Spinner A lands on 2 and Spinner B does not land on 2, we use the probabilities from the tree:
- The probability of Spinner A landing on 2 is ( \frac{1}{3} ).
- The probability of Spinner B not landing on 2 is ( \frac{2}{3} ).
These are independent events, so we multiply the probabilities:
Thus, the final probability is ( \frac{2}{9} ).