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To take your probability exam you buy pencils both from factory A and factory B. Unfortunately...

To take your probability exam you buy pencils both from factory A and factory B.
Unfortunately not all the pencils from either factory have unbroken lead. Each pencil that factory A produces is perfect independently with probability 0.8 and each pencil that factory B produces is perfect independently with an unknown probability p, which
you know is within 0.1 of the probability for factory A. You buy 100 pencils from factory A and 48 pencils from factory B. The approximate probability that you have at least 51 more perfect pencils that came from factory A than the number of perfect pencils that came from factory B, is 0.0968. Find an approximately value of p probability that a pencil from factory B is perfect.

math   Statistics-And-Probability   
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