JEE Main 2003 — Probability Question with Solution

X : Mr. A selected wining horse

$$\overline{X}$$ : Mr. A did not select wining horse

Mr. A selected two horses, now probability of not wining the first horse which Mr. A choses = $$\frac{4}{5}$$

And probability of not wining the second horse also which Mr. A choses = $$\frac{3}{4}$$ (Here Mr. A out of remaining 4 horses choses one horse among 3 horses which did not win)

$$\therefore$$ $$P(\overline{X})=\frac{4}{5}\times \frac{3}{4}$$

$$\therefore$$ $$P(X)=1-P(\overline{X})$$

$$=1-\frac{4}{5}\times \frac{3}{4}$$

$$=1-\frac{3}{5}$$

$$=\frac{2}{5}$$