This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're pointing out a specific part of the calculation. Let's clarify. The probability P(X=0) represents the probability of getting zero heads when tossing four fair coins. There is only one way to get zero heads: TTTT (Tail, Tail, Tail, Tail). Since there are 2^4 = 16 total possible outcomes when tossing four coins, the probability of getting zero heads is (1)/(16). So, P(X=0) = (1)/(16) is correct. The term 0 ((1)/(16)) in the expectation calculation E[X] = x P(X=x) is the contribution of x=0 to the sum. This term simplifies to 0, but it uses the correct probability P(X=0) = (1)/(16). If P(X=0) were 0/16, it would mean it's impossible to get zero heads, which is not true for four coin tosses. What else can I help with?