Question

three coins are rolled simultaneously find the probability that tail appears on the middle one​

Answer 1

Answer:

1/2

Even though the coins may be indistinguishable and the toss is simultaneous, as a mental model we can refer to them as coins A, B, and C. We break the event “not more than one tails” into the elementary phenomena regarding A, B, and C.

First note that “not more than one” breaks into “exactly zero or exactly one”. These events are called disjoint, meaning they are mutually exclusive, which allows their probabilities to add when we want to compute that one or the other happens. The probability of zero tails is the probability that all of the coins are heads:

1/2×1/2×1/2=1/8  

The event “exactly one tails” is decomposed into the three phenomena “only A is tails”, “only B is tails”, and “only C is tails”. Each of these similarly has probability 1/8, so the probability that one of them happens is 3/8.

Hence the probability of at most one tails is

1/8+3/8=1/2  

You can also get this by symmetry: the probability of exactly one tails must be the same as exactly one heads, and the probability of zero tails must be the same as zero heads, so these two possibilities are half of the total probability of 1.

Explanation:

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Answer 2

Answer:

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