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# Probabilty and Randomness

Problem #1
What is the chance of getting eight or fewer tails on 10 flips of a coin?
Problem #2
A salesperson has been losing 25% of potential sales. In a study of 20 random sales contacts from this salesperson, what is the probability of finding 4 or more successful sales?
Problem #3
An automatic transmission repair shop had an established standard to do a certain type of repair. They hired a new mechanic. After six months, they sampled 12 of the new mechanicĂ˘??s repair times versus the standard repair. The new mechanic took more than the standard time on eight of the 12 samples. How confident would the repair shop be in judging that the higher times were due to shop performance rather than to random causes? In your opinion, should the shop keep the new mechanic?
Expectations:
1. Answer questions with clarity and show the detailed steps for calculation.

#### Solution Preview

1. Prob. of getting 8 or fewer tails = 1 - prob. of getting 9 tails - prob. of getting 10 tails.

Here we use the binomals distribution to find out the probabilities of getting 9 and 10 tails.

P(X = x) = (nCx)(p^x)[(1-p)^(n-x)], where n is total number of trials, x is the number of successes you want, and p is the probability of getting a single success. nCx means n choose x, which is the binomial coefficient. nCx=n!/[x!(n-x)!], where n! = n(n-1)(n-2)...1, 0! = 1 by definition.

So P(X = 9) = (10C9)[(0.5)^9][0.5^1] = 0.0098, and P(X = 10) = ...

#### Solution Summary

Probabilty and Randomness

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