A bag contains 4 red, 3 yellow and 2 purple discs. A disc is taken, at random, from the bag and is not replaced. A second disc is then taken, at random, from the bag. Calculate the probability that the two discs taken from the bag are different colours?
please help
please help
The first thing to do is to convert these possibilities into a tree diagram, like the one below which I did in Word:
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To calculate the probability that the two discs taken from the bag are different colors, we need to consider the total number of possible outcomes and the number of favorable outcomes where the discs are of different colors.
Total number of discs = 4 (red) + 3 (yellow) + 2 (purple) = 9
The probability of choosing a disc of a different color on the second draw depends on the color of the disc chosen in the first draw. We can calculate this probability separately for each color.
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Probability of choosing a red disc first: Probability of choosing a non-red disc on the second draw = (Total non-red discs) / (Total remaining discs after the first draw) = (3 yellow + 2 purple) / (9 total discs - 1 disc already drawn) = (3 + 2) / 8
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Probability of choosing a yellow disc first: Probability of choosing a non-yellow disc on the second draw = (Total non-yellow discs) / (Total remaining discs after the first draw) = (4 red + 2 purple) / (9 total discs - 1 disc already drawn) = (4 + 2) / 8
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Probability of choosing a purple disc first: Probability of choosing a non-purple disc on the second draw = (Total non-purple discs) / (Total remaining discs after the first draw) = (4 red + 3 yellow) / (9 total discs - 1 disc already drawn) = (4 + 3) / 8
Now, we calculate the overall probability by considering all three cases and summing their probabilities: Overall probability = (Probability of choosing red first) + (Probability of choosing yellow first) + (Probability of choosing purple first) = [(3 + 2) / 8] + [(4 + 2) / 8] + [(4 + 3) / 8]
= (5/8) + (6/8) + (7/8) = 18/8
Therefore, the probability that the two discs taken from the bag are different colors is 18/8, which simplifies to 9/4.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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