Question

For a certain candy, 10% of the pieces are yellow, 15% are red, 20% are blue, 15% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it is brown? it is yellow or blue? it is not green? it is striped? b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a row, what is the probability that they are all brown? the third one is the first one that is red? none are yellow? at least one is green? a) The probability that it is brown is (Round to three decimal places as needed.) The probability that it is yellow or blue is (Round to three decimal places as needed.) The probability that it is not green is (Round to three decimal places as needed.) The probability that it is striped is (Round to three decimal places as needed.) b) The probability of picking three brown candies is (Round to three decimal places as needed.) The probability of the third one being the first red one is (Round to three decimal places as needed.) The probability that none are yellow is (Round to three decimal places as needed.) The probability of at least one green candy is I. (Round to three decimal places as needed.)

Answer 1

The calculation of probabilities for different colored candies within the context of a set distribution involves understanding and applying the fundamental rules of probability. Various scenarios, such as the likelihood of picking candies of a certain color or a sequence of colors, can be computed using these principles.

Step-by-step explanation:

The subject matter in question relates to the concept of probability within the field of mathematics, specifically geared towards a high school level understanding. When confronted with the distribution of colors in a set of candies and how these distributions affect the likelihood of different events, we can calculate the probabilities of particular outcomes based on the given percentages or counts.

For example, if the percentage of brown candies is not directly provided, you would subtract the sum of the percentages of all other colors from 100%. For the second part, the probability of multiple events happening in sequence (such as picking three candies of the same color in a row) can be determined by using the rules of probability for independent events - that is, multiplying the probabilities of each event occurring separately, assuming an infinite supply. This is because each pick is independent, and the probability remains unchanged after each pick.

When considering events like 'none are yellow' or 'at least one is green', you would use complementary probabilities. For example, the probability of 'at least one is green' is the complement of the probability that none are green.