If a heads is flipped, then the coin is flipped 4 more times and the number...

If a heads is flipped, then the coin is flipped 4 more times and the number of heads flipped is noted; otherwise (i.e., a tails is flipped on the initial flip), then the coin is flipped 3 more times and the result of each flip (i.e., heads or tails) is noted successively. How many possible outcomes are in the sample space of this experiment?

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Expert Solution

case 1 : A coin is flipped once. The result is a head. The coin is flipped 4 more times.

number of possible outcomes in the sample space = 2*2*2*2 = 16

case 2 : A coin is flipped once. The result is a tail. The coin is flipped 3 more times.

number of possible outcomes in the sample space = 2*2*2 = 8

number of possible outcomes are in the sample space of this experiment = 16 + 8 = 24

if you count only distinct outcomes then

case 1 : A coin is flipped once. The result is a head. The coin is flipped 4 more times.

number of possible distinct outcomes in the sample space = 5 (Reason : Tossing a coin 4 times implies the number of heads can take only value 0,1,2,3,4.)

case 2 : A coin is flipped once. The result is a tail. The coin is flipped 3 more times.

number of possible outcomes in the sample space = 2*2*2 = 8

number of possible outcomes are in the sample space of this experiment = 5 + 8 = 13

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orchestra answered 1 year ago

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