An experiment consists of tossing a coin and drawing a card, with the card-drawing stage dependent on the result of the coin toss. If heads occurs, then a card is selected at random from the clubs and spades suits. If tails occurs, then a card is selected at random from the hearts and diamonds suits. What is the size of the sample space of this two-stage experiment?
A.
26
B.
52
C.
104
D.
208

Question

An experiment consists of tossing a coin and drawing a card, with the card-drawing stage dependent on the result of the coin toss. If heads occurs, then a card is selected at random from the clubs and spades suits. If tails occurs, then a card is selected at random from the hearts and diamonds suits. What is the size of the sample space of this two-stage experiment?
A. 
26
B. 
52
C. 
104
D. 
208

Mercury · Answer

thoughts? notice half the deck is being assigned to heads and half the deck is being assigned to tails

thinking about this like a probability tree, we have heads-club-ace, heads-club-2, heads-club-3 etc. for 26 total outcomes when you combine the club and spade suits. repeat the same logic for the tails-heart and tails-spade set and add up the total outcomes.