Expected ValueSuppose you are conducting an experiment by tossing two coins simultaneously. You note down the number of tails in each toss. How many tails can you expect on average in each experiment?Note: Round off your answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.
Question
Expected ValueSuppose you are conducting an experiment by tossing two coins simultaneously. You note down the number of tails in each toss. How many tails can you expect on average in each experiment?Note: Round off your answer to two decimal places. If your answer is 1.333333, write 1.33 in the box.
Solution
To calculate the expected value, we first need to understand all the possible outcomes of tossing two coins simultaneously. They are:
- Two Heads (HH)
- Head and Tail (HT)
- Tail and Head (TH)
- Two Tails (TT)
Now, we assign the number of tails to each outcome:
- Two Heads (HH) - 0 tails
- Head and Tail (HT) - 1 tail
- Tail and Head (TH) - 1 tail
- Two Tails (TT) - 2 tails
Next, we calculate the probability of each outcome. Since there are 4 possible outcomes, the probability of each is 1/4 or 0.25.
Finally, we calculate the expected value by multiplying each outcome by its probability and adding them up:
(0 tails * 0.25) + (1 tail * 0.25) + (1 tail * 0.25) + (2 tails * 0.25) = 0 + 0.25 + 0.25 + 0.5 = 1 tail
So, on average, you can expect 1 tail in each experiment.
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