Question 1209659
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17​% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. 
Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ 
(a) exactly​ three, 
(b) at least​ four, 
(c) less than eight. 
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        In the post by @CPhill,  all calculations for part  (b)  are incorrect.

        The answer for part  (b)  is incorrect, too.


        Below I placed my correct calculations.



<pre>
**(b) At least four:**

This means x = 4, 5, 6, ..., 12.  It's easier to calculate the complement and subtract from 1:

P(x ≥ 4) = 1 - P(x < 4)
P(x ≥ 4) = 1 - [P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)]

*   P(x = 0) = (12C0) * (0.17)^0 * (0.83)^12 ≈ 0.10689
*   P(x = 1) = (12C1) * (0.17)^1 * (0.83)^11 ≈ 0.26272
*   P(x = 2) = (12C2) * (0.17)^2 * (0.83)^10 ≈ 0.29595
*   P(x = 3) ≈ 0.201 (calculated above)

P(x ≥ 4) = 1 - (0.10689 + 0.26272 + 0.29595 + 0.201)
P(x ≥ 4) = 1 - 0.867
P(x ≥ 4) ≈ 0.133
</pre>

Corrected.