Answer:
a. Exactly three = 0.00117
b. At least four = 0.00457
c. Less than eight = 0.222
Step-by-step explanation:
a. Since 26% U.S adults favour unmanned drone by police agencies, if 12 such adults are selected at random, then the probability that exactly 3 of them will favour the use of the unmanned drones will be:
(26/100)^3 × (74/100)^9
This is because there's a 26% chance that the first 3 adults picked out of the randomly selected twelve will be in support of the unmanned drone and there's a 74% (100%-26%) chance that the other 9 (12-3) adults that will be picked will not be in support.
Therefore (26/100)^3 × (74/100)^9
= 0.0176 × 0.0665
= 0.00117
b. In this case, the probability that at least four U.S adults out of the randomly selected 12 will support the idea of an unmanned drone:
(26/100)^4
Now each of the four adults have a 26/100 chance of supporting the idea of an unmanned drone by police agencies. It doesn't matter what the other 8 adults support.
So the probability that at least four out of the 12 will be in support:
= (26/100)^4
= 0.00457
c. The probability that less than eight out of the randomly selected 12 will be in support means that at least 5 out of the selected 12 adults will be against the idea of an unmanned drone by police agencies. It doesn't matter what the other 7 are in support of. The 5 that will not be in support will have a 74/100 chance of being picked.
The probability that at least 5 non-supporters are picked
= (74/100)^5
= 0.74^5
= 0.222
