Three coins are tossed once. Let A denote the event 'three heads show", $\mathrm{B}$ denote the event "two heads and one tail show", $\mathrm{C}$ denote the event" three tails show and D denote the event 'a head shows on the first coin". Which events are
(i) mutually exclusive?
(ii) simple?
(iii) Compound?

Answer

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Algebra

NCERT Class 11 - Math

Chapter 16

Probability

Section 2

Random Experiments

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Video Transcript

And this problem When three coins are tossed the samples piece. Yes, is given by. It's it's it's HD H. It's HD at stating the H. T. T. H. PhD and tick tick tick. So this is the sample space A. Which is the event. Not three heads show. So he is nothing. But uhh. Ahh. Let us look at B. B. Is the event That two heads in one tail show. So it is HD HD H. R. P. H. Let us look at sea Where three deals show to see is nothing but PTT. Let us look at the such that beast. Even that head occurs in the first coin. So it is. Ahh. HD H. It's HD and HD T. Now what do we observe? We observe. So let me write the observations there. Yeah. First observation is that a intersection B. Is a null set. Second intersection C. Is also a null set than a intersection B. Yes. Ahh. Which is not an L. Sec. Look at the 4th observation which is be intersection C. We see that this is an all set with the observation be intersection B. It has elements like. HD H and it's it's steam. So it is not a null set. Let's look at sea intersection D. And that is all nelson. So we say that for the force part, event A and B. Event A, N, C. Even BNC and event Cnd are all mutually exclusive. This can be directly seen from the observations. Let us look at the 2nd part. We know It is a simple amount when there is only one sample point or in assembles piece. That's why A. And C. Uh huh. Simple events. And it's a component that if there are more than one sample points, so be India compound That's all.

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