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An unbiased coin is tossed 3 times, the expected value of the number of heads is
- a)2.5
- b)1.0
- c)1.5
- d)2
Correct answer is option 'C'. Can you explain this answer?
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An unbiased coin is tossed 3 times, theexpected value of the number of...
Solution:
To find the expected value of the number of heads when an unbiased coin is tossed 3 times, we can use the formula:
Expected Value = (Number of Heads)(Probability of getting a Head) + (Number of Tails)(Probability of getting a Tail)
Let's break this down:
Number of Heads: This can be any number from 0 to 3, since we are tossing the coin 3 times.
Probability of getting a Head: Since the coin is unbiased, the probability of getting a Head on any given toss is 0.5.
Number of Tails: This will be the remaining number of tosses after we count the number of Heads. For example, if we get 2 Heads, then we have 1 remaining toss, which must be a Tail.
Probability of getting a Tail: Since the coin is unbiased, the probability of getting a Tail on any given toss is also 0.5.
Using this information, we can calculate the expected value as follows:
Expected Value = (0)(0.5)^3 + (1)(3)(0.5)^3 + (2)(3)(0.5)^3 + (3)(0.5)^3
Expected Value = 0 + 0.375 + 0.375 + 0
Expected Value = 0.75
Therefore, the expected value of the number of heads is 0.75, which is closest to option 'C' (1.5).
To find the expected value of the number of heads when an unbiased coin is tossed 3 times, we can use the formula:
Expected Value = (Number of Heads)(Probability of getting a Head) + (Number of Tails)(Probability of getting a Tail)
Let's break this down:
Number of Heads: This can be any number from 0 to 3, since we are tossing the coin 3 times.
Probability of getting a Head: Since the coin is unbiased, the probability of getting a Head on any given toss is 0.5.
Number of Tails: This will be the remaining number of tosses after we count the number of Heads. For example, if we get 2 Heads, then we have 1 remaining toss, which must be a Tail.
Probability of getting a Tail: Since the coin is unbiased, the probability of getting a Tail on any given toss is also 0.5.
Using this information, we can calculate the expected value as follows:
Expected Value = (0)(0.5)^3 + (1)(3)(0.5)^3 + (2)(3)(0.5)^3 + (3)(0.5)^3
Expected Value = 0 + 0.375 + 0.375 + 0
Expected Value = 0.75
Therefore, the expected value of the number of heads is 0.75, which is closest to option 'C' (1.5).
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An unbiased coin is tossed 3 times, theexpected value of the number of heads isa)2.5b)1.0c)1.5d)2Correct answer is option 'C'. Can you explain this answer?
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