Assume you are writing a mechanic in a video game where an item obtained from a

Question

Assume you are writing a mechanic in a video game where an item obtained from a treasure chest is random. For each time the player opens the treasure chest, the item received could be a rare item (with probability 0.3), a common item (with probability 0.6), and an empty chest (with probability 0.1). The dropped items occur independently (i.e. the events are memoryless). Answer the following questions about the behavior of the dropped items: a. What is the probability that the player obtains a common item, a rare item, and an empty chest, in that order, in three consecutive searches? b. What is the probability that the player obtains a common item, a rare item, and an empty chest, in any order, in three consecutive searches? c. What is the probability that the player will no a common item or empty chest after five searches? d. What is the probability that the player will obtain an empty chest or common item at least once after five searches?

Explanation / Answer

a. Calculating the given probability = P(Common item at first) * P( Rare item at second) * P( Empty chest inend)

Pr = 0.3 * 0.6 * 0.1 = 0.018

b. calculating the given probability = 3! * ( 0.3 * 0.6 * 0.1) = 0.108

c. Pr( That player will not obtain a common item or empty chest after 5 searches that means he will only get rare prize in each first 5 searches) = 5C5 (0.3)5 = 0.00243

d. Pr( That player will obtain a common item or empty cheast at least once after 5 searches) = 1 - Pr(That player will not obtain a common item or empty chest after 5 searches that means he will only get rare prize in each first 5 searches) = 1 - 0.00243 = 0.99757

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