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a fair coin is tossed 9 times the probability that at least 5 consecutive heads occure is.............?

a fair coin is tossed 9 times the probability that at least 5 consecutive heads occure is.............?

Grade:11

1 Answers

Aditya
13 Points
7 years ago
Total outcome=2^n as n=9 ;dn =2^9=512
case-1
let exactly 5 cons head occur = H H H H H _ _ _ _ 
at 6 th position must be tail and 7,8,9 has no codition( because only 5 cons head)
hence= HHHHHT____ this three position can be HHH, HHT, HTH, THH, HTT, THT, TTH , TTT=》 8 ways
Case-2
let exactly 6 cons head occur=》HHHHHH_ _ _=》7th position must be tail( only 6 cons head)
=》HHHHHHT_ _ this two can be HH, HT,TH,TT=》4 ways
Similarly for 7 cons head =》2 ways required
and for 8 cons head =》only 1 way
Heance total ways = 8+4+2+1=15
Required answer= 15/512 
 

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