Single Choice

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is.

A$$\displaystyle\frac{63}{64}$$
B$$\displaystyle\frac{1}{2}$$
C$$\displaystyle\frac{127}{128}$$
Correct Answer
D$$\displaystyle\frac{255}{256}$$

Solution

$$p=P(H)=\dfrac {1}{2}$$, $$q=P(T)=1_{/2}$$

$$P$$ (at least one head & one tail)
$$P(1 < H < 7)=P(1 < H)$$

$$=1-[\displaystyle p(H)=0 $$ and $$ p(H)=8]$$
$$=1-\left[2\cdot (1{/2})^8\right]$$

$$=1-\left[2\cdot \displaystyle\frac{1}{16\times 16}\right]$$

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

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

SIMILAR QUESTIONS

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