First slide

Theorems of probability

Question

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

Moderate

A

3/16
B

5/32
C

3/18
D

1/8

Solution

$Let H denote the head, T the tail and * any of the head$ $or tail. Then, P (H) = 1 / 2, P (T) = 1 / 2 and P (*) = 1 . For at least$
$four consecutive heads, we should have any of the following$
patterns:
Since all the above cases are mutually exclusive, the probability of getting at least four consecutive heads (on adding) is
$1 / 16 + 3 / 32 = 5 / 32$

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