Question

The letters T, C and A can be written in several different orders
a) Write the letters in as many different orders as possible.
b) If a computer writes these three letters in a random order, calculate
probability that:
(i) the letters will be written in alphabetical order
(ii) the letter T is written before both the letters A and C
(iii) the letter C is written after the letter A
(iv) the computer will spell the word CAT.​

Answer 1

Answer:

a)ACT,ATC

CAT,CTA

TAC,TCA

Probability of an event=No of desired outcomes/Total no of possible outcomes

b)i) Probability that letters will be in alphabetical order (i.e. ACT)= 1/6

ii) Probability that letter T is before both A and C(i.e. TCA,TAC) = 2/6= 1/3

iii) Probability that letter C is written after A (i.e. ACT,TAC,ATC) =3/6=1/2

iv) Probability that computer will spell word CAT=1/6