Cody has two bags of counters, bag $$\(\mathbf{A}\)$$ and bag $$\(\mathbf{B}\)$$. Each of the counters has either an odd number or an even number written on it. There are 10 counters in bag $$\(\mathbf{A}\)$$ and 7 of these counters have an odd number written on them. There are 12 counters in bag $$\(\mathbf{B}\)$$ and 7 of these counters have an odd number written on them. Cody is going to take at random a counter from bag $$\(\mathbf{A}\)$$ and a counter from bag $$\(\mathbf{B}\)$$. (a) Complete the probability tree diagram. (2) (b) Calculate the probability that the total of the numbers on the two counters will be an odd number. (3) Harriet also has a bag of counters. Each of her counters also has either an odd number or an even number written on it. Harriet is going to take at random a counter from her bag of counters. The probability that the number on each of Cody's two counters and the number on Harriet's counter will all be even is $$\(\frac{3}{100}\)$$ (c) Find the least number of counters that Harriet has in her bag. Show your working clearly. (3)

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