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).

Answer 1

The options for this question are missing here are the options:

A) 1/8

B) 2/8

C) 5/8

D) 7/8

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

Answer 2

Given:

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 is the random variable which is zero if no T has another T adjacent to it, and is one otherwise.

Let Y denote the random variable that counts the number of T's in the three tosses.

The correct answer is option B that is 2/8.