# A company has discovered that a recent batch of batteries had manufacturing​ flaws, and has issued a recall.

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A company has discovered that a recent batch of batteries had manufacturing​ flaws, and has issued a recall. In a group of 15 batteries covered by the​ recall, 6 are dead. Two batteries at random are chosen from the package of 15.

​a) Has the assumption of independence been​ met? Explain.
​b) Create a probability model for the number of good batteries chosen.
​c) What's the expected number of good​ batteries?
​d) What's the standard​ deviation?

The standard deviation of this problem?

sqrt(1.86  - 1.2^2) =  0.648

The expected number of good Batteries = 0*0.143 + 1*0.514 + 2*0.343 = 1.2

a.

No, because the outcome for the first battery affects the probability that the second battery is dead.

b. Create a probality Model table

Hint: Determine the probabilities associated with each possible value. Since the batteries are chosen without​ replacement, use conditional probabilities and the General Multiplication​ Rule, given​ below, to find each probability.

 X(Number good) P(X=x) 0 0.143 1 0.514 2 0.343

p(X =0) =  6/15 * 5/14  = 0.143

P(X=1)  =  6/15*9/14 + 9/15 * 6/14  = 0.514

P(X = 2) =  9/15 * 8/14  = 0.3423