Question

A card is drawn from a standard deck of 52 playing cards. If the card is a club, a fair coin is flipped 9 times and the number of heads flipped is noted. If it is not a club, the coin is only flipped 3 times, but this time the result of each flip is noted. The card drawn is not noted in either case. How many elements are in the sample space for this experiment?

Answer 1

Answer: There are 18 elements in the sample space for this experiment

Step-by-step explanation:

Total cards = 52

Total outcomes on tossing a coin = 2   [1 head , 1 tail]

If the card is a club, a fair coin is flipped 9 times and the number of heads flipped is noted (but card drawn is not noted)).

Possible outcomes for heads = 0,1,2,...,9

So sample space for this event = {0,1,2,3,4,5,6,7,8,9} (Total 10 elements ) (i)

If it is not a club, the coin is only flipped 3 times, but this time the result of each flip is noted(but card drawn is not noted).

Sample space with all possible outcomes ={TTT,TTH, THT, HTT, HTH,HHT,THH,HHH}   (Total 18 elements )  (ii)

From (i) and (ii), Total elements in the sample space for this experiment = 10+8 = 18

Hence, there are 18 elements in the sample space for this experiment