Probability 2

Probability Tree

Probability Tree is a very good tool in finding the probability of an occurrence of an event provided -
1) The outcomes or circumstances of an event are very small in number
2) The experiment should not be repeated large number of times

Note:
The depth of the tree is the number of times the experiment is repeated.
Example: Flipping coins 5 times.

The width of the tree is the count of all possible outcomes of an event.
Example: H & T are the 2 outcome of flipping the coin.

Lets take an example and solve the probability using Probability Tree

Find the probability of two heads occuring on two consecutive flips of coins, i.e., P(HH)

From the above probability tree the total out comes or circumstances of flipping coin twice is 4. Out of the 4 outcomes, the total number of times we get HH is 1, so the P(HH) = 1/4.

Another way to look at it is the probability of first flip leading to heads is 1/2, and this remains the same even during the second flip because both heads and tails are equally probable and they are not mutually exclusive so it leads to 1/2 * 1/2 = 1/4.

Note we multiply the probabilities because the events are not mutually exclusive.

Similary P(1H, 1T) = 2/4 = 1/2

P(HHHHH) = 1/2*1/2*1/2*1/2*1/2 = 1/32

P(Out of 7 flips, heads should not come even once) = p(TTTTTTT) = 1/128