kapilnegi wrote:

When a coin is tossed for 5 times, what is the probability that after the first tossing, every outcome will be different from the previous one?

a. 1/16

b. 1/24

c. 1/32

d. 1/48

e. 1/64

a or c?

There are two ways of thinking about this:

The first one considers the first flip as a given and thus not part of the probability. In this case there are only 4 remaining flips that are left to chance, each having a 1 out of 2 chance of being different from the previous

--> (1/2)^4 =

1/16The second possibility considers the first flip as part of the probability, thus there are five flips that are left to chance. However, if you count the first flip as being left to chance then there are also 2 different scenarios / starting points --> heads or tails:

The first flip has a 1/2 chance of being heads and a 1/2 chance of being tails

1/2 chance of

heads being the starting point: then (1/2)^4 of being different in each subsequent flip --> (1/2)^5 = 1/32

1/2 chance of

tails being the starting point: then (1/2)^4 of being different in each subsequent flip --> (1/2)^5 = 1/32

Since either one of these can happen (heads first or tails first) you have to add their probabilities together --> 2/32 =

1/16 Either approach we take, we get 1/16 as the answer.

A
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Factorials were someone's attempt to make math look exciting!!!