Which of the following random variables is geometric?

a. The number of times I have to roll a single die to get two $6\mathrm{s}$

b. The number of cards I deal from a well-shuffled deck of 52 cards to get a heart

c. The number of digits I read in a randomly selected row of the random digits table to

get a 7

d. The number of $7\mathrm{s}$ in a row of 40 random digits

e. The number of $6\mathrm{s}$ I get if I roll a die 10 times

If the trials are constantly repeated until a success happens and the probability of success in each trial is the same, then the random variable follows a geometric distribution.

• The cards are shuffled in option 'b' until a heart appears. The cards are shuffled in this scenario until a success (heart) happens, hence it is a case of geometric distribution.
• Option 'c' involves reading the digits to obtain a 7. It is an example of geometric distribution since the digits are read repeatedly until a success occurs $(=7)$.

• Option (a) A die is rolled until two 6s appear. It is evident here that the trials are repeated for more than a success $=6$. As a result, it isn't an instance of geometric distribution.
• There is no first success constraint in option 'd' and 'e'. The random variable in this case is concerned with the number of counts of success. As a result, option d and e do not have a geometric distribution.