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A bag contains 4 red counters and 3 blue counters only - OCR - GCSE Maths - Question 17 - 2019 - Paper 2
Question 17
A bag contains 4 red counters and 3 blue counters only. Jack picks a counter at random and then replaces it. Jack then picks a second counter at random. (a) Complet... show full transcript
Worked Solution & Example Answer:A bag contains 4 red counters and 3 blue counters only - OCR - GCSE Maths - Question 17 - 2019 - Paper 2
Step 1
Complete the tree diagram.
Answer
For the first pick, the probabilities are:
- Red: ( \frac{4}{7} )
- Blue: ( \frac{3}{7} )
For the second pick: If the first pick is Red:
- Red: ( \frac{4}{7} )
- Blue: ( \frac{3}{7} )
If the first pick is Blue:
- Red: ( \frac{4}{7} )
- Blue: ( \frac{3}{7} )
Thus, the completed tree diagram is as follows:
First pick
Red (4/7)
Red (4/7)
Blue (3/7)
Blue (3/7)
Red (4/7)
Blue (3/7)
Step 2
Work out the probability that Jack picks two red counters.
Answer
To calculate the probability that Jack picks two red counters, we consider the outcomes:
- Probability of picking Red first and Red second: [ P(RR) = P(R) \times P(R|R) = \frac{4}{7} \times \frac{4}{7} = \frac{16}{49} ]
Hence, the probability that Jack picks two red counters is ( \frac{16}{49} ).