Q3.(12) One store notes that the probability of some type of error in a telephone order is 0.2. A supervisor randomly selects telephone orders and carefully inspects each one.  What is the

1. Use this table for the following questions:                        Female      Male         TotalShort Hair       20              40             60 Long Hair        30              10             40 Total                50              50             100 a. Complete a total probability table.b. Complete a row probability tablec. Complete a column probability table.d. The probability that a student does not have long hair. _________e. The probability that a student is male or has short hair. ________f. The probability that a student is a female and has long hair. _________g. The probability that a student is male, given that the student has long hair. _________h. The probability that a student has long hair, given that the student is male. _________i. Of all the female students, the probability that a student has short hair. ________j. Of all students with long hair, the probability that a student is female. _________k. The probability that a student is female or has long hair.…

12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. The following table may (or may not) be useful: k 0 1 2 3 4 1 4 6 4 1 4Ck (a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. (c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.

14. Colors of Christmas: In a Christmas display, the probability that all lights are the same color is 0.50; that 2 colors are used is 0.40; and that 3 or more colors are used is 0.10. If a sample of 10 displays is selected, find the probability that 5 have only 1 color of light, 3 have 2 colors. and 2 have 3 or more colors.