A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head, we throw a die. Find the sample space of this experiment.
A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head, we throw a die. Find the sample space of this experiment.

According to the question, A coin is tossed and there is box which contains 2 red and 3 black balls.

When coin is tossed, the outcomes will be {H, T}

According to question, if tail is turned up, then a ball is drawn from a box.

So, sample for this experiment will be S1 = {(T, R1) (T, R2) (T, B1) (T, B2) (T, B3)}

Now, If Head is turned up, and then die is rolled.

Sample space for this experiment will be S2 = {(H, 1) (H, 2) (H, 3) (H, 4) (H, 5) (H, 6)}

The required sample space will be S = S1 ⋃ S2

So,

S = {(T, R1), (T, R2), (T, B1), (T, B2), (T, B3), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}

∴ S is the elementary events associated with the given experiment.