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Standard XII

Mathematics

Simple and Compound Event

Three coins a...

Question

Three coins are tossed once. Describe the following 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.

(i) Which pairs of events are mutually exclusive?

(ii) Which events arc elementary events?

(iii) Which events are compound events?

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Solution

A - Getting three heads a {HHH} - 1

B - Getting two heads and one tail = {HHT,THH, HTH} = 3

C - Getting three tails = {TTT} = 1

D - Getting a head on the first coin =
(HHH, HHT, HTH, HTT) = 4

(i) We know that A and B are said to be mutually exclusive if $A \cap B$

(a) A and B
(b) A and C
(c) B and C
(d) C and D are munually exclusive

(ii) A and C are elementary events.

(iii) Clearly B and D are union of three events and 4 events respectively.

$∴$ B and D are compound events.

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