Question 981805: 23% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! exactly 3
12C3 (0.23)^3(0.77)^9=0.2547
At least 4 means all others except 0,1,2,3.
We know what 3 is
for 2: 12C2*(0.23)^2*(0.77)^10=0.2558
for 1: 12*.23*.77^11=0.1557
for 0: .77^12=0.0434
Those 4 sum to 0.7096
At least 4 is 1-0.7096, since it is the complement. It is 0.2904.
For less than 8
probability of 4 is 12C4(0.23)^4(0.77)^8=0.1712
probability of 5=12C5(0.23)^5(0.77)^7=0.0818
probability of 6=12C6(0.23)^6*(0.77)^6=0.0285
probability of 7=12C7(0.23)^7(0.77)^5=0.0073
These 4 sum to 0.2888
The other 4 sum to 0.7096
The probability it is less than 8 is their sum or 0.9984.
|
|
|
