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Q.
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
Probability
Solution:
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 $= 42$