Question

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

Answer 1

There are $2+10+5=17$ tickets in a box.

$$P(A\ draws \ bad)=\dfrac{2}{17}$$

If A draws bad

$$P(B\ draws \ good\ or\ very\ good)=\dfrac{15}{16}$$

$$P(A\ draws \ good)=\dfrac{10}{17}$$

If A draws good

$$P(B\ draws\ very\ good)=\dfrac{5}{16}$$

The probability that Mr. B draws a better ticket

$$\dfrac{2}{17}(\dfrac{15}{16})+\dfrac{10}{17}(\dfrac{5}{16})=\dfrac{5}{17}$$