In a particular town, 25% of all bikes are road bikes, 40% are cross bikes, and 35% are mountain bikes. Of all road bikes, 70% are blue and the rest are green. Of all cross bikes, 10% are green, 35% are red, and the remainder are blue. A fifth of all mountain bikes are green.If you pick a single bike at random, what’s the probability that it would be green? (keep your answer to 3 significant digits, e.g., 0.XXX).
Question
In a particular town, 25% of all bikes are road bikes, 40% are cross bikes, and 35% are mountain bikes. Of all road bikes, 70% are blue and the rest are green. Of all cross bikes, 10% are green, 35% are red, and the remainder are blue. A fifth of all mountain bikes are green.If you pick a single bike at random, what’s the probability that it would be green? (keep your answer to 3 significant digits, e.g., 0.XXX).
Solution
To solve this problem, we need to calculate the probability of each type of bike being green and then add those probabilities together.
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Road bikes: 25% of all bikes are road bikes and 30% of these are green (since 70% are blue, the rest, which is 30%, must be green). So, the probability of picking a green road bike is 0.25 * 0.30 = 0.075 or 7.5%.
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Cross bikes: 40% of all bikes are cross bikes and 10% of these are green. So, the probability of picking a green cross bike is 0.40 * 0.10 = 0.040 or 4%.
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Mountain bikes: 35% of all bikes are mountain bikes and 20% of these are green (since a fifth is the same as 20%). So, the probability of picking a green mountain bike is 0.35 * 0.20 = 0.070 or 7%.
Now, add these probabilities together to get the total probability of picking a green bike:
0.075 (green road bikes) + 0.040 (green cross bikes) + 0.070 (green mountain bikes) = 0.185 or 18.5%.
So, the probability that a randomly selected bike would be green is 0.185.
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