Question

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.

Answer 1

Given: A coin is tossed and there is box which contains 2 red and 3 black balls.

When coin is tossed, there are 2 outcomes {H, T}

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

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

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

So, sample space for this experiment 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.