Clyde has a cone-shaped party hat. The height of the hat is 10 inches, and the radius of the base of the hat is 4 inches. What i
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Answer:
Assume that all the coins involved here are fair coins.
a) Probability of finding the "odd" person in one round: .
b) Probability of finding the "odd" person in the th round:
.
c) Expected number of rounds: .
Step-by-step explanation:
<h3>a)</h3>To decide the "odd" person, either of the following must happen:
- There are
heads and
tail, or
- There are
Assume that the coins here all are all fair. In other words, each has a chance of landing on the head and a
The binomial distribution can model the outcome of coin-tosses. The chance of getting
heads out of
- The chance of getting
.
- The chance of getting
.
These two events are mutually-exclusive. would be the chance that either of them will occur. That's the same as the chance of determining the "odd" person in one round.
Since the coins here are all fair, the chance of determining the "odd" person would be in all rounds.
When the chance of getting a success in each round is the same, the geometric distribution would give the probability of getting the first success (that is, to find the "odd" person) in the
th round:
. That's the same as the probability of getting one success after
unsuccessful attempts.
In this case, . Therefore, the probability of succeeding on round
round would be
.
Let is the chance of success on each round in a geometric distribution. The expected value of that distribution would be
.
In this case, since , the expected value would be
.