a coin is tossed until a head appears or the tail appears 4 times in succession. Find the probability distribution of the no. of tosses ?
Answers
P(1) = 1/2 , P(2) = 1/4 , P(3) =1/8 , P(4) = 1/8 probability distribution of the no. of tosses
Step-by-step explanation:
a coin is tossed until a head appears or the tail appears 4 times in succession.
Possible number of tosses
( number of tosses until head appears or 4 Tails in succession so maximum possible number of tosses = 4)
1 Toss - H
2 Toss - TH
3 Toss - TTH
4 Toss - TTTT or TTTH
P(1) = 1/2
P(2) = (1/2)(1/2) = 1/4
P(3) = (1/2)(1/2)(1/2) = 1/8
P(4) = (1/2)(1/2)(1/2)(1/2) + (1/2)(1/2)(1/2)(1/2) = 1/16 + 1/16 = 1/8
Expected number of tosses = 1 * 1/2 + 2 * 1/4 + 3*1/8 + 4*1/8
= 1/2 + 1/2 + 3/8 + 1/2
= 3/2 + 3/8
= (15/8)
= 1.875 is expected number of tosses
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