Suppose 80% of all voters support Jones, and you pick 4 voters at random.?

Suppose 80% of all voters support Jones, and you pick 4 voters at random.


a. what is the probability that all 4 support Jones?


b.what's the probability that the first voter supports jones, thenthe next 2 don't support jones, then the last one does, in that exact order?


c.What's the probability that 2 voters support jones?


d. What's the probability that none of the voters support jones?

Suppose 80% of all voters support Jones, and you pick 4 voters at random.?
Since all 4 voters are independent of each other, we can multiply their probabilities:





a) P{all support} = 0.8*0.8*0.8*0.8 = 41%





b) P{ ... } = 0.8*0.2*0.2*0.8 = 2.6%





d) Similar to (a): P{None support} = 0.2*0.2*0.2*0.2 = 1.6%





c) P{2 support}


Need to know how many ways you can choose 2 from 4 (a


combination, denoted nCr). In this case, we have 2C4 = 6.


P{2 support} = 2C4 * 0.8*0.8*0.2*0.2


= 6 * 0.8*0.8*0.2*0.2


= 15.4%
Reply:a. 0.8 * 0.8 * 0.8 * 0.8 = 40.96%


b. 0.8 * 0.2 * 0.2 * 0.8 = 2.56%


c. 0.8 * 0.8 * 0.2 * 0.2 = 2.56% for exacxtly 2 supporters


c. 1 - (0.2 * 0.2 * 0.2) = 99.2% for at least 2 supporters


d. 0.2 * 0.2 * 0.2 * 0.2 = 0.16%