Question

A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Then, the total number of outcomes for this experiment is

• A. $40$
• B. $42$
• C. $41$
• D. $43$

Answer 1

Answer: (B)

The sample space associated with the given random experiment is given by
$S=\{(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,4)$,
$(2,5),(2,6),(3,1),(3,2),(3,4),(3,5),(3,6),(4,1),(4,2)$,
$(4,3),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,6),(6,1)$,
$(6,2),(6,3),(6,4),(6,5)\}$
Now, when outcome is a doublet, then a coin is tossed.
So, sample space $=\{(11,H),(11,T),(22,H),(22,T)$,
$(33,H),(33,T).(44,H),(44,T),(55,H),(55,T),(66,H),(66,T)\}$
Hence, total number of sample points $=42$