Probability:

You throw two fair six-sided dice.

What is the probability that one score is less than 4 and the other score is greater than 4?

My working:

S = Score 1

T = Score 2

P(S < 4) = 1/2

P(T > 4) = 1/3

P(S < 4 ∩ T > 4) = 1/2 * 1/3 = 1/6

Where have I gone wrong?

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.