A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is 2/3 in each toss. What is the probability of obtaining an even number of heads in tosses, zero being treated as an evennumber?a)121/243b)122/243c)124/243d)125/243e)128/243Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Probability of obtaining an even number of heads in tosses

To calculate the probability of obtaining an even number of heads in tosses, we can use the concept of binomial distribution.

Calculating the Probability

- Let's consider the probability of getting a head as p = 2/3 and the probability of getting a tail as q = 1/3.
- The total number of tosses is n, and we want to find the probability of getting an even number of heads.
- The probability of getting an even number of heads can be calculated by summing the probabilities of getting 0, 2, 4, ... heads.
- The general formula for the probability of getting k heads in n tosses is given by P(k) = C(n,k) * (p^k) * (q^(n-k)), where C(n,k) is the binomial coefficient.
- Since we want the probability of getting an even number of heads, we need to sum the probabilities of getting 0, 2, 4, ... heads.
- The probability of getting an even number of heads can be calculated as P(even) = P(0) + P(2) + P(4) + ... = ΣP(2k), where k ranges from 0 to n/2.
- By calculating the individual probabilities and summing them up, we find that the probability of obtaining an even number of heads is 121/243.

Therefore, the correct answer is option 'A' (121/243).

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