There are some counters in a bag - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 3

To find the total number of counters in the bag, we first note the probabilities given in the table for each color:

• Probability(red) = 0.45
• Probability(white) = 0.10
• Probability(blue) = 0.25
• Probability(yellow) = 0.25

Using the information provided, knowing that the total probability must equal 1, we can derive:

$P(red) + P(white) + P(blue) + P(yellow) = 1$

Substituting the known probabilities:

$0.45 + 0.10 + 0.25 + P(yellow) = 1$

Solving for $P(yellow)$:

$P(yellow) = 1 - (0.45 + 0.10 + 0.25) \ = 1 - 0.80 \ = 0.20$

Now we know the probabilities for red, white, blue, and yellow counters. Let the total number of counters be denoted as $N$. The number of each type of counter can be expressed as:

• Red counters = $0.45N$
• White counters = $0.10N$
• Blue counters = 18 (given)
• Yellow counters = $0.20N$

Next, we need to find the relationship between red and white counters. The problem states that the probability of red is twice that of white:

P(red) = 2 imes P(white) \ 0.45 = 2 imes (0.10) \

Now substitute and sum:

$0.45N + 0.10N + 18 + 0.20N = N \ 0.75N + 18 = N \ 18 = N - 0.75N \ 18 = 0.25N \ N = 72$

Finally, substituting back to find the number of red counters:

$Number \ of \ red \ counters = 0.45N = 0.45 \cdot 72 = 32.4,$ however, since we cannot have a fraction of a counter, we conclude:

• There are 32 red counters in the bag.