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Answer :
Final answer:
The probability of finding exactly four infested samples in a row is about 0.0028. The probability of finding exactly three infested samples amongst four successive samples is about 0.048. both probabilities were calculated using the laws of probability theory and rounded to the appropriate number of decimal places.
Explanation:
The subject of this question is Mathematics specifically a category referred to as probability theory. As per the details of the question, the probability that the plant tissues are infested by spider mites in a randomly selected area is 23% (or 0.23 in decimal form). This probability is consistent throughout the entire plant.
(a) To find the probability of exactly four successive samples showing signs of infestation, we consider only these four specific trials in a sequence of six trials. For each sample, the probability of infestation is independent and remains 0.23. Therefore, the probability of four successive infested areas is (0.23)^4. Rounding to four decimal places, this is approximately 0.0028.
(b) For the second scenario, where exactly three out of four successive samples show signs of infestation, there are four spots the non-infested sample could be in (at the start, between two infested samples, or at the end). Thus, the probability is 4 * ((0.23)^3) * (1-0.23). rounding to three decimal places, it's approximately 0.048.
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