Q81 / 160 · TS EAMCET 2004 · Mathematics

An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is

  • Correct answer
    A
    $\frac{1}{2}$
  • B
    $\frac{1}{4}$
  • C
    $\frac{1}{8}$
  • D
    $\frac{3}{8}$

Solution

We are getting a odd number of point, if it will comes (two head, one tail and three tail) $$ \because \quad P(H)=P(T)=\frac{1}{2} $$ $\therefore$ Required probability $=$ Probability of getting two heads and one tail + Probability of all three tails $$ \begin{aligned} & ={ }^3 C_2\left(\frac{1}{2}\right)^2\left(\frac{1}{2}\right)^1+\left(\frac{1}{2}\right)^3 \\ & =3\left(\frac{1}{2}\right)^3+\left(\frac{1}{2}\right)^3=\frac{3}{8}+\frac{1}{8}=\frac{1}{2} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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