Algebra

Probability

Medium

applied

A fair coin is tossed until a head or five tails occur. The probability distribution of the number of tosses is,

X	1	2	3	4	5
P(X)	1/2	1/4	1/8	1/16	1/16

X	0	1	2	3	4
P(X)	1/6	1/6	1/6	1/6	1/6

X	-1	0	1	2	3
P(X)	3/6	4/6	1/6	7/6	3/6

X	2	3	4	5	6
P(X)	2/4	3/6	2/6	3/4	1/4

✅ Correct Option: 1

Tossing stops at the first head or after five tails, so $X$ takes values 1 to 5. For $X=1,2,3,4$ the probability of that many tosses is $\left(\frac12\right)^X$ , giving $\frac12,\frac14,\frac18,\frac{1}{16}$ . $X=5$ covers both TTTTH and TTTTT, so its probability is $2\times\frac{1}{32}=\frac{1}{16}$ , and the total is 1.

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Solution

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