Week 307 (28th July 2023)

Kate and Nicola are selling raffle tickets at the summer fete.  

In total 50 raffle tickets are sold.  

The tickets sold are numbered from 1 to 50.  

The raffle tickets are placed in a box for the draw.  

One raffle ticket is selected at random and not replaced in the box. 

A second ticket is then randomly selected.  

Find the probability that one of the tickets drawn is odd and the other is even. 


Probability that 1st ticket is odd = 25/50 = ½      

Probability that 1st ticket is even = 25/50 = ½   

Probability that 2nd ticket is odd given 1st was even = 25/49      

Probability that 2nd ticket is even given 1st was odd = 25/49 

If we need the probability that one ticket is odd and the other even, the combinations are:  

  • 1st ticket was even and 2nd was odd 
  • 1st ticket was odd and 2nd was even 
  • Probability that one ticket is odd and the other even = (1/2 x 25/49) + (1/2 x 25/49) = 25/49