Question

A compound experiment consists of tossing a coin, drawing a letter at random from the alphabet, and then tossing two coins. What is the probability of getting a tail, the letter T, and then two tails? 1/156 1/208 1/52

Answer 1

I believe the answer is "1/208"

Answer 2

Given that there are three different games played.

Game 1: Toss a coin

Game 2: Drawing a letter at random from the alphabet

Game 3: Toss two coins

From first game we need to get "tail"

we know that there are two possible cases when tossing any coin {Head , Tail}

So probability of getting tail = 1/2

From second game we need to get letter "T"

we know that there are total 26 alphabets

So probability of getting letter T = 1/26

From third game we need to get two "tail"

Possible cases are {HH, HT, TH, TT} which are 4

H means Head T means tail. We see that double tail occurs only once from 4 possible cases

So probability of getting two tail = 1/4

Now we can combine all the results to find the probability of getting a tail, the letter T, and then two tails

$Probability = \frac{1}{2}\cdot\frac{1}{26}\cdot\frac{1}{4} = \frac{1}{208}$

Hence final answer will be $\frac{1}{208}$