When 2 products are chosen among the batch of stale (s) and a fresh (f) products,average of 4 possible results are calculated as; sf: 0.21, fs:0.21, ss:0,05 and ff:053.X, indicating that the product is fresh; a)Find the probability P(1< X< 3) b)Find the probability P(X < 1)

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When 2 products are chosen among the batch of stale (s) and a fresh (f)
products,average of 4 possible results are calculated as; sf: 0.21, fs:0.21,
ss:0,05 and ff:053.X, indicating that the product is fresh;
a)Find the probability P(1< X< 3)
b)Find the probability P(X < 1)
Transcribed Image Text:When 2 products are chosen among the batch of stale (s) and a fresh (f) products,average of 4 possible results are calculated as; sf: 0.21, fs:0.21, ss:0,05 and ff:053.X, indicating that the product is fresh; a)Find the probability P(1< X< 3) b)Find the probability P(X < 1)
Expert Solution
Step 1

Given-

There are four outcomes of the two products chosen with the probability stated as-

stale , fresh : 0.21

fresh, stale : 0.21

stale, stale : 0.05

fresh, fresh : 0.53

Step 2

a) X indicating that the product is fresh. Calculating 

Probability homework question answer, step 2, image 1

As, X should be greater than or equal to 1 but less than 3 (the total number of fresh products chosen can be less than or equal to so its indifferent whether X is above 2) , so the total outcomes are: sf, fs, ff.

Summing up the stated probabilities.

0.21(s,f) + 0.21(f,s) + 0.53(f,f) 

So, the probability comes out to be 0.95.

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