Question

A fair coin is tossed three times and a T (for tails) or H (for heads) is recorded, giving us a list of length 3. Let X be the random variable which is zero if no T has another T adjacent to it, and is one othetwise. Let Y denote the random variable that counts the number of T's in the three tosses. Find P(X=1, Y=2).
A) 1/8
B) 2/8
C) 5/8
D) 7/8

Answer 1

When a fair coin is tossed 3 times, the outcomes are

(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

EAch of the above outcome has an equal probability = 1/8

X =1 implies there is a T adjacent to a T

and Y=2 implies there are 3 tails

P(X=1, y=2) = P(two TTs are adjacent, there are 3 Ts}

There is only one outcome satisfying this.  TTT

Hence Prob = 1/8

Answer 2

Answer:

When the coin will be tossed three times in a row this will be the outcome:

TTT

TTH

THT

THH

HTT

HTH

HHT

HHH

X = 1 tells us that T is adjacent to T

and Y = 2 tells us that there are two T's

and because of this we made two conclusions:

TTH, HTT

P (X = 1, Y = 2) = 2/8

So the answer for this question is B: 2/8