Answer to Question #184202 in Statistics and Probability for Ayesha

Question

Mr.A draws a ticket from a box containing 2 bad,10 good and 5 ver good tickets. If Mr.B draw the next ticket, what is his chance of a better performance than Mr .A??

Answer 1

The probability that Mr.A will draw the ticket is the following:

for the bad ticket: $\frac{2}{17}$ = 11.76%, and so the chance of better performance of Mr.B increases (because there will be less bad tickets, but the same amount of good and very good)

for the very good ticket: $\frac{5}{17}$ = 29.41%, and so the chance of better performance of Mr.B equals 0 (because it is not possible to draw a better one than very good)

for the good ticket: $\frac{10}{17}$ = 58.82%, and so the chances of performance of Mr.B:

for the bad ticket: $\frac{2}{16}$ = 12.5%

for the good ticket: $\frac{9}{16}$ = 56.25%

for the very good ticket: $\frac{5}{16}$ = 31.25%

so the chance of drawing a better ticket increased by (31.25 - 29.41) = 1.84%, the chance of drawing a worse ticket increased by (12.5 - 11.76) = 0.74%. Totaly, the chance of drawing a better ticket increase more, than a worse ticket.

So, the chance of better performance is $\frac{2}{17} + \frac{10}{17} = \frac{12}{17} =70.59$%

Answer: 70.59%.