Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# Three Coins Are Tossed Once. Describe the Events Associated with this Random Experiment: (Ii) Which Events Are Elementary Events? - Mathematics

Three coins are tossed once. Describe the events associated with this random experiment:

A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.

(ii) Which events are elementary events?

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#### Solution

When three coins are tossed, the sample space is given by
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Accordingly, we have:
A = {HHH}
B = {HHT, HTH, THH}
C = {TTT}
D = {HHH, HHT, HTH, HTT}

Now, we observe that
A ∩ B = Φ; A ∩ C = Φ; A ∩ D = {HHH} ≠ Φ; B ∩ C = Φ; B ∩ D = {HHT, {HTH} ≠ Φ and C ∩ D = Φ

(ii) If an event has only one sample point of a sample space, it is called an elementary event.
Thus, A and C are elementary events.

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.2 | Q 3.2 | Page 15
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