Consider 3 boxes, each of which contains 4 balls; in particular, box 1 contains 4 white balls, box 2 contains 3 white balls and
1 red ball, box 3 contains 2 white balls and 2 red balls. Frank chooses a box at random. If boxes 1 and 3 are chosen, Frank extracts 2 balls without replacement. If box 2 is chosen Frank extracts 2 balls with replacement. USE ONLY THE CONDITIONAL PROBABILITY FORMALISM and derive an expression for the probability that the 2 extracted balls are red.
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Answer:
Step-by-step explanation:
Given that a popcorn company builds a machine to fill 1 kg bags of popcorn. They test the first hundred bags filled and find that the bags have an average weight of 1,040 grams with a standard deviation of 25 grams.
i.e. Sample mean = 1040 and
Sample std dev s = 25 gm
Sample size n = 100
Hence by central limit theorem we have the sample mean follows a normal distribution with mean =1040 and std dev = s = 25 gm
Normal curve would be with mean 1040 and std deviatin 25
b) P(X>1115)
= 1-0.9987
=0.0013
i.e. 0.13% would receive a bag that had a weight greater than 1115 grams