1A special type of password consists of four different lette

1.A special type of password consists of four different letters of the alphabet, where each letter is used only once. How many different possible passwords are there?

2.In a survey of 70 students, 20 used brand A, 45 used brand B, and 15 used both brands A and B.

(round to two decimal places).

(a) What proportion (probability) used either brand A or brand B.

(b) What proportion (probability) used neither brand A nor brand B; that is not brand A and not brand B.

3.A bag contains 16 marbles, 11 black and 5 white. Two marbles are drawn without replacement, which means that the first one is not put back before the second one is drawn. (round answers to three decimal places.)

(a) What is the probability that both marbles are black?

(b) What is the probability that exactly one marble is black?

Solution

1) As there are total 26 alphabets , _ _ _ _ we need to fill these 4 spaces , 1st space can be filled by any of 26 alphabets ,the next by the remaining 25 and so on
so, different possible passwords= 26*25*24*23 = 358800

2)
a)   P(either A or B) =P(A) +P(B) - P(A and B) = (20+45-15) /70= 50/70   =5/7
b)   P(not A and not B) = 1 - P(not (not A and not B)) = 1 - P(A or B) = 1-5/7 =2/7

3)
a) P( both marbles are black) = 11/16 * 10/15 = 0.458
b) P( exactly one is black)= 11/16* 5/15 * 2 ( as both side occurence, black can come first or second) = 0.458