A bag only contains red, blue, yellow and white counters - OCR - GCSE Maths - Question 13 - 2020 - Paper 1
Question 13
A bag only contains red, blue, yellow and white counters.
A counter is taken at random from the bag.
The table shows the probability it is red and the probability it... show full transcript
Worked Solution & Example Answer:A bag only contains red, blue, yellow and white counters - OCR - GCSE Maths - Question 13 - 2020 - Paper 1
Step 1
Calculate the total probability for yellow and white counters.
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Answer
The total probability for all counters must equal 1.
Let the probability of yellow be denoted as P(yellow) = y, and the probability of white be denoted as P(white) = w.
From the table, we have the equation:
0.24+0.34+y+w=1
This simplifies to:
y+w=1−(0.24+0.34)=1−0.58=0.42
Step 2
Express yellow and white probabilities in terms of w.
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From the problem, we know there are twice as many yellow counters as white counters. Therefore, we can express yellow in terms of white:
y=2w
Substituting this into the equation gives:
2w+w=0.42
This simplifies to:
3w=0.42
Solving for w yields:
w = rac{0.42}{3} = 0.14.
Step 3
Determine the probability of yellow counters.
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Now substituting back to find yellow:
y=2w=2(0.14)=0.28.
Step 4
Fill in the probabilities for yellow and white in the table.
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Now we can fill in the probabilities in the table:
