Probability Examples Coin and Dice

In this class, We discuss Probability Examples Coin and Dice.

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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