Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Probability - Arrays.
Test Yourself 1.


 

Boxes 1. At a Federal Election recently, five candidates stood in a particular seat. Their names were allocated at random to the Ballot paper.

We will describe their order as being A, B, C, D and then E.

(i) What was the probability that Candidate A was drawn first?

(ii) What is the probability that the candidates were arranged in the order A, E, B, D and then C ?

Answer.(i) Pr (A first) = 1/5.
(ii) Pr(given order) = 1/120.
  2. Nikita plans to wear jeans with a T-shirt and a jumper. She has two pairs of jeans, four T-shirts and three jumpers.

How many different outfits can she wear?

Answer.2 × 4 × 3 = 24 outfits.
  3. The internal telephone numbers in a large business contain 5 digits.

(i) How many different telephone numbers are possible?

What is the probability that:

(ii) telephone numbers do not end in a 9?

(iii) the telephone number starts with 555?

 
 

The wild animal enclosure in a zoo has 5 lions and 3 jaguars. It has constructed 8 cages in which to keep these lovely animals.

If the lions are too large for the jaguars' cages, in how many ways can the animals be placed in the cages?
   
  7. I have a friend who forgot her 4 digit PIN number for the ATM. Each digit of her PIN is of course one of the integers 0 to 9.

(i) What is the probability of my friend correctly guessing her PIN?

(ii) What is the probability of her guessing at least one digit correctly?

(iii) She now thinks that there is a 6 or a 7 as either the second or the last digit. What is now her probabiity of correctly guessing her PIN?

(iv) Now, with a sigh of relief, my friend remembers the four digits in her PIN but not their order. What is now her chance of guessing her PIN correctly?

Answer.(i) Pr(correct) = 1/10,000
(ii) 1 - (1/10)4 = 3,439/10,000
(iii) 1/1,000
(iv) 1/24