Probability Examples Coin and Dice
In this class, We discuss Probability Examples Coin and Dice.
The reader should know probability, sample space, and event. Click Here.
Random Experiment:
Tossing two unbiased coins is our experiment.
1) Find the probability of getting exactly one head.
To find the probability value, we find the sample space.
Sample space = {HH, HT, TH, TT}
Number of elements in sample space N(S) = 4
E = Event = Getting exactly one head
E = {HT, TH}
N(E) = Number of elements in the event.
N(E) = 2
Probability of the event E = N(E)/N(S)
P(E) = N(E)/N(S)
P(E) = 2/4 = 1/2 = 0.5
2) Find the probability of getting atleast one head?
For the same random experiment.
N(E) = {HH, HT, TH} = 3
N(S) = 4
P(E) = N(E)/N(S) = 3/4 = 0.75
Random Experiment: Roll an unbiased dice
1) Probability of getting 1 or 2 on the dice.
Sample space = {1, 2, 3, 4, 5, 6} = S
N(S) = 6
Event = {1,2} = E
N(E) = 2
P(E) = N(E)/N(S) = 2/6
Random Experiment:
Roll two unbiased dice.
Sample space = {(1,1), (1,2), . . .,(6,6)} = S
N(S) = 36
1) Probability of getting sum value showed on the dice is 10
Event = E = sum of values on the dice = 10
E = {(5,5), (6,4), (4,6)}
N(E) = 3
P(E) = N(E)/N(S)
P(E) = 3/36
P(E) = 1/13
2) Probability of getting sum value perfect square.
Event = E = {(1,3), (3,1), (2,2),(3,6), (6,3), (4,5), (5,4)}
N(E) = 7
P(E) = N(E)/N(S) = 7/36
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