The numbers 2,3,5,6, and 8 are written on five cards and these are placed on a table. Two of these cards are selected at random to form a two digit number. List the sample space and find the probability that the number formed is (i) odd, (ii) divisible by 7, (iii) prime, (iv) greater than 54.
The sample space consists of these 20 numbers:
{23, 25, 26, 28,
32, 35, 36, 38
52, 53, 56, 58
62, 63, 65, 68,
82, 83, 85, 86}
(i) The odd ones in the sample space are these 8:
{23, 25, 35, 53, 63, 65, 83, 85}
So the probability is 8 out of 20 or which reduces to .
(ii) The ones divisible by 7 are these 4
{28, 35, 56, 63}
So the probability is 4 out of 20 or which reduces to .
(iii) The ones that are prime are these 2:
{23, 83}
So the probability is 2 out of 20 or which reduces to .
(iv) The ones that are greater than 54 are these 10
{56, 58, 62, 63, 65, 68, 82, 83, 85, 86}
So the probability is 10 out of 20 or which reduces to .
Edwin