When six coins are tossed simultaneously, the probability of getting at least 4 heads is

When six coins are tossed simultaneously, the probability of getting at least 4 heads is
  1. $\frac{11}{64}$
  2. $\frac{15}{64}$
  3. $\frac{11}{32}$
  4. $\frac{15}{32}$

Solution

Total possible chances $=2^6=64$ Required probability $ \begin{gathered} =P(\text { Getting } 4 \text { Heads })+P(\text { Getting } 5 \text { Heads }) \\ \{\text { TTHHHH }\} \quad\{\text { THHHHH }\} \\ +P(\text { Getting } 6 \text { Heads }) \end{gathered} $ \{Нннннн \} $ \begin{aligned} & =\frac{6 !}{2 ! 4 !}+\frac{6 !}{64 ! 5 !}+\frac{\frac{6 !}{6 !}}{64}=\frac{15}{64}+\frac{6}{64}+\frac{1}{64} \\ & =\frac{22}{64}=\frac{11}{32} \end{aligned} $ Hence, option (3) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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