First slide

Theorems of probability

Question

A coin is flipped seven times. If the probability that it comes up head at least 4 times in a row is

Moderate

A

5/23
B

5/32
C

5/30
D

5/27

Solution

Let, E: head comes at least 4 times in a row
Possible outcomes are
$\begin{matrix} HHHH \times \times \times \\ THHHH \times \times \\ \times THHHH \times \\ \times \times THHHH \end{matrix}$ (where x means F or T)
$∴ P (E) = \frac{1}{16} + \frac{3}{32} = \frac{5}{32}$

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