Question

1.Your Username for your company computer is three letters followed by five single digit numbers. The Letters can be repeated but the digits cannot be repeated. Find total possible number of usernames for your company"s computer system.

2.If a pair of fair dice is rolled find following probability that a number other than seven or eleven is rolled such that it is given that one of the two die is a two or a four.?

3.It is estimated that 2% pregnancies are the result of in vitro fertilization. The chance of multiple births from in vitro fertilization is 48%. The chance of multiple births from normal methods is 3%.

a) What is the probability a couple used in vitro fertilization and it resulted in a non-multiple birth?

b) If a multiple birth did not occur, what is the probability that it is the result of normal methods?

Answer 1

1:

There are 26 different letters and 10 different digits.

Each letter can be selected in 26 ways. Since digit cannot be repeated so first digit can be repeated in 10 ways, second in 9 ways, third in 8 ways and so on.

Total  possible number of usernames for your company"s computer system is

26*26*26*10*9*8*7*6= 531,498,240

2:

Following is the possible outcomes when we sum the outcomes of two rolls of die:

The outcomes such that one of the two die is a two or a four is

Out of above 16 outcomes, 4 outcomes shows sum 7 or 11 so

P(sum seven or eleven | one of the two die is a two or a four) = 4/ 16 = 0.25

3:

(a)

Let V shows the event that pregnancy is the result of in vitro fertilization and M shows the event pregnancy is the result of in normal method. Let M shows the event of multiple births. So

P(V) = 0.02, P(M|V) = 0.48, P(M|N) = 0.03

By the complement rule,

P(N) = 1 - P(V) = 0.98

P(M' |V) = 1-P(M|V) = 1 - 0.48 = 0.52

P(M' |N) = 1-P(M|N) = 1 - 0.03 = 0.97

The  probability a couple used in vitro fertilization and it resulted in a non-multiple birth is

P(V and M') = P(M' |V)P(V) = 0.52 * 0.02 = 0.0104

(b)

The probability that it is the result of normal methods, given that a multiple birth did not occur is