Question

If you flip a coin ten times, how many different sequences of heads and tails are possible? a. 2 superscript 9 baseline = 512 b. 10 squared = 100 c. 10 squared = 1024 d. 2 superscript 10 baseline = 1024 please select the best answer from the choices provided a b c d

1. diemthu
The total number of different possible sequences of heads and tails when a coin is flipped 10 times is 1024.
According to the given question.
A coin is flipped 10 times.
As we know that a sample space or sequence is a collection or a set of possible outcomes of a random experiment.
If a coin is flipped once, then the number of possible sequences or outcomes will be 2 (either head or a tail).
Since, the coin is flipped 10 times in a row.
Thereofore,
The number of different possible sequences of heads and tails
= 2^10
= 1024
Where, 2 is the number of possible sequences when a coin is flipped once and 10 is the number of trials.
⇒ 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 ×2 × 2 = 1024
Hence, the total number of different possible sequences of heads and tails when a coin is flipped 10 times is 1024.
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