State whether each of the following defined events is an elementary event. a) Ob
ID: 3272864 • Letter: S
Question
State whether each of the following defined events is an elementary event. a) Obtaining a seven when a pair of dice are rolled. b) Obtaining two heads when three coins are flipped. c) Obtaining an ace when a card is selected at random from a deck of cards. d) Obtaining a two of spades when a card is selected at random from a deck of cards. e) Obtaining a two when a pair of dice are rolled. f) Obtaining three heads when three coins are flipped. g) Observing a value less than ten when a random voltage is observed.Explanation / Answer
An elementary event is the event which contains only a single outcome in the sample space.
a) Obtaining a 7 when a pair of dice is thrown
A sum of 7 could be obtained in many ways: 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3. Therefore this particular event wont be an elementary event.
b) Obtaining 2 heads when 3 coins are tossed. This can be obtained as:
{ HHT, HTH, THH }
Therefore this particular event wont be an elementary event. ( as there are 3 outcomes in this event )
c) Obtaining an Ace when a card is selected from the deck of cards - This can happen in 4 outcomes as there are 4 different aces in the deck of cards.
Therefore this particular event wont be an elementary event.
d) Obtaining 2 of spades when a card is selected at random from a deck of cards. This can happen only in 1 way as there is only one 2 of spade.
Therefore this particular event is an elementary event.
e) Obtaining a two when a pair of dice are rolled.
This can happen only in one way that is 1 + 1
Therefore this particular event is an elementary event.
f) 3 heads could be only obtained as HHH
Therefore this particular event is an elementary event.
g) Observing a value less than ten when a random voltage is observed. Voltage could be any number less than 10, clearly as there are so many voltages less than 10,
Therefore this particular event wont be an elementary event.
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