Lars likes to catch yabbies at the river. The weight of any given yabby that Lars catches is uniformly distributed between 36 and 74 grams. Assume that the weight of a caught yabby is independent from yabby to yabby.Lars managed to catch 3 yabbies today. Find the probability that the first yabby Lars caught weighed more than 73 grams or the second yabby Lars caught weighed between 54 and 70 grams.
Question
Lars likes to catch yabbies at the river. The weight of any given yabby that Lars catches is uniformly distributed between 36 and 74 grams. Assume that the weight of a caught yabby is independent from yabby to yabby.Lars managed to catch 3 yabbies today. Find the probability that the first yabby Lars caught weighed more than 73 grams or the second yabby Lars caught weighed between 54 and 70 grams.
Solution
Step 1: Understand the problem
The problem is asking for the probability of two independent events: the first yabby weighing more than 73 grams and the second yabby weighing between 54 and 70 grams.
Step 2: Calculate the probability of each event
The weight of the yabbies is uniformly distributed between 36 and 74 grams. This means that the probability of any given weight within this range is the same.
For the first yabby to weigh more than 73 grams, we need to calculate the probability of the yabby weighing between 73 and 74 grams. Since the weight is uniformly distributed, this probability is (74-73)/(74-36) = 1/38.
For the second yabby to weigh between 54 and 70 grams, we need to calculate the probability of the yabby weighing between these two weights. Again, since the weight is uniformly distributed, this probability is (70-54)/(74-36) = 16/38.
Step 3: Combine the probabilities
Since these are independent events, we can add the probabilities together to get the total probability.
So, the probability that the first yabby Lars caught weighed more than 73 grams or the second yabby Lars caught weighed between 54 and 70 grams is 1/38 + 16/38 = 17/38.
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