(a) Briefly discuss the binomial probability distribution.

(b) A coin is flipped 12 times: what is the probability ofgetting:

i. no heads; and)

ii. no more than 3 heads?

Over the past 10 years two golfers have had an ongoing battle asto who the better golfer is. Curtley Weird has won 120 of their 200matches, while Dave Chilly has won 70 with 10 of them ending inties. Because Dave is going overseas they decide to play atournament of five matches to establish once and for all who thebetter player is.

Find the probabilities that:

(a) Dave wins at least three of the matches;

(b) Curtley wins no more than two games; and

(c) all of the games end in a tie.

(a) Discuss probability, independence and mutual exclusivity,giving examples to illustrate your answer.

i. How many ways are there of choosing a committee of threepeople from a club of ten?

ii. How many ways are there of selecting from those three peoplea president, secretary and treasurer?

iii. Illustrate your answer to the second part of the questionwith a tree diagram.

An ice-cream vendor on the beachfront knows from long experiencethat the average rate of ice-cream sales is 12 per hour. If, withtwo hours to go at work, she finds herself with only fiveice-creams in stock, what are the probabilities that

(a) she runs out before the end of the day;

(b) she sells exactly what she has in stock by the end of theday without any excess demand after she sells the last one; and

(c) she doesn't sell any?

A company applying for medical aid cover counts that 70 of its140 male employees smoke. Of the 100 female employees, 20 smoke.What is the probability that an employee chosen at random

(a) is female and smokes; (2)

b) does not smoke; and

(c) is male or smokes?

In a true or false assignment of six questions you are obligedto get at least four correct to pass. If you guess the answers tothe questions, what are the probabilities that:

a) you pass; (4)

(b) you get at least 50% of the answers correct; and

(c) you get no more than two correct? (3)

onist claims that he gets 10 calls every five minutes. Todemonstrate this to his boss he makes a tape lasting five minutes.What are the probabilities that he gets:

(a) no calls in the five minutes; (2)

(b) less than three calls; and (5)

(c) exactly 10 calls? (

Assume that matric marks are standardised to have a mean of 52%and a standard deviation of 16% (and assume that they have a normaldistribution). In a class of 100 students estimate how many ofthem:

(a) pass (in other words get more than 33,3%);

(b) get A's (more than 80%); and

(c) get B's (between 70% and 80%).

As manager of a company you know that the distribution ofcompletion times for an assembly operation is a normal distributionwith a mean of 120 seconds and a standard deviation of 20 seconds.If you have to award bonuses to the top 10% of your workers whattime would you use as a cut-off time? [6]