an unbiased coin is tossed 12 times the probability that atleast 7 consecutive
heads show up is
Answers
Given : an unbiased coin is tossed 12 times
To Find : probability that atleast 7 consecutive heads show up
Solution:
unbiased coin
Probability of head = 1/2
Probability of tail = 1/2
Tossed 12 times total ways = 2¹²
atleast 7 consecutive heads show up
There can be cases
Consecutive Heads staring from 1st , 2nd , 3rd , 4th , 5th and 6th.
below - means it can be either head or tail.
HHHHHHH - - - - - = (1/2)⁷(1)⁵
THHHHHHH - - - - (1/2)(1/2)⁷(1)⁴
-THHHHHHH - - - (1)¹(1/2)(1/2)⁷(1)³
--THHHHHHH - - (1)²(1/2)(1/2)⁷(1)²
---THHHHHHH - (1)³(1/2)(1/2)⁷(1)
----THHHHHHH (1)⁴(1/2)(1/2)⁷
(1/2)⁷ ( 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2)
= 7 /2⁸
= 7/256
Probability of atleast 7 coins showing head = 7/256
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