JEE Main 2017 — Probability Question with Solution

An unbiased coin is tossed 8 times which is same as 8 coins tossed 1 times.

$$\therefore$$ Possible no. of out come = 2⁸

$$\therefore$$ Sample space = 2⁸

Here in this condition, all head or all tail out come is not acceptable.

No. of times all head can occur

(H H H H H H H H) = 1

$$\therefore$$ Probability (all head) = $$\frac{1}{2^8}$$ = $$\frac{1}{256}$$

No. of times all tail can occur

(T T T T T T T T) = 1

$$\therefore$$ Probability (all tail) = $$\frac{1}{2^8}$$ = $$\frac{1}{256}$$

$$\therefore$$ Required probability

= 1 $$-$$ (P (All head) + P (All tail))

= 1 $$-$$ ( $$\frac{1}{256}$$ + $$\frac{1}{256}$$)

= 1 $$-$$ $$\frac{1}{128}$$

= $$\frac{127}{128}$$