10 If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is

Question

10 If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is

BlackTom AI · Accepted Answer

When evaluating a simple coin-toss scenario, a key principle is that each flip is independent of previous ones. 
Option 1 says the fifth-head probability is larger than the probability of tails. Since a fair penny has equal chances for heads and tails on any given flip, both events have probability 0.5, so one is not larger than the other. 
Option 2 states 1/32, which would correspond to the probability of getting heads on five consecutive tosses (a cumulative sequence), not just a single fifth toss. This confuses a compound event with a single-trial probability. 
Option 3 asserts 0.5. This aligns with the independence of flips and the fair coin assumption: the fifth trial remains heads with probability 0.5 regardless of the past four outcomes. 
Option 4 claims zero, implying heads can never occur on the fifth trial, which contradicts the basic probability of a fair coin and the possibility of either outcome on any trial. 
In summary, the only option that matches the standard model of a fair, independent coin is the one that reflects a 50% chance for heads on any single flip, while the other choices rely on misinterpreting independence, sequence probabilities, or impossibility.

10 If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is 单项选择题

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