Probability
Probability is a branch of mathematics deals with occurrence of random event.
Probability means possibility of happening. When a coin is tossed, possibilities to turn a head
or tail.
Here tossing a coin is a random experiment.
Basic definitions and examples
Outcome and sample space
A possible result of a random experiment is called its event.
Consider tossing a coin, there are 2 events head and tail. Sample space is { H, T}
Condenser rolling die, possibilities are getting 1, 2,3, 4, 5,6.
Here sample space = { 1,2,3,4,5,6}
Examples1. : Two coins are tossed once. Find a sample space.
Since either coin can turn up Head (H) or Tail (T), the possible outcomes may be
Heads on both coins = (H, H)
Heads on first coin and Tail on the other = (H, T)
Tail on first coin and Head on the other = (T, H)
Tail on bothe coins = (T, T)
Thus the sample space is S= {(HH, HT, TH, TT}
Example 2. A die is tossed 2 times. Find the sample space.
1 on 1st die and 1 on 2nd die (1,1)
1 on 1st die and 2 on 2nd die (1, 2)
1 on 1st die and 3 on 2nd die (1, 3)
1 on 1st die and 4 on 2nd die (1, 4)
1 on 1st die and 5 on 2nd die (1, 5)
1 on 1st die and 6 on 2nd die (1, 6)
Similarly (2, 1), (2, 2)(2, 3), (2, 4),(2, 5),(2, 6)
(3, 1), (3,2), (3,3), (3, 4), (3, 5), (3, 6)
(4,1), (4,2), (4, 3), (4,4), (4,5), (4, 6)
(5, 1), (5, 2),(5, 3), (5, 4), (5, 5), (5, 6)
(6,1), (6, 2), 6, 3), (6,4), 6, 5), (6, 6)
sample space consists of 36 outcomes.
Probability is a branch of mathematics deals with occurrence of random event.
Probability means possibility of happening. When a coin is tossed, possibilities to turn a head
or tail.
Here tossing a coin is a random experiment.
Basic definitions and examples
Outcome and sample space
A possible result of a random experiment is called its event.
Consider tossing a coin, there are 2 events head and tail. Sample space is { H, T}
Condenser rolling die, possibilities are getting 1, 2,3, 4, 5,6.
Here sample space = { 1,2,3,4,5,6}
Examples1. : Two coins are tossed once. Find a sample space.
Since either coin can turn up Head (H) or Tail (T), the possible outcomes may be
Heads on both coins = (H, H)
Heads on first coin and Tail on the other = (H, T)
Tail on first coin and Head on the other = (T, H)
Tail on bothe coins = (T, T)
Thus the sample space is S= {(HH, HT, TH, TT}
Example 2. A die is tossed 2 times. Find the sample space.
1 on 1st die and 1 on 2nd die (1,1)
1 on 1st die and 2 on 2nd die (1, 2)
1 on 1st die and 3 on 2nd die (1, 3)
1 on 1st die and 4 on 2nd die (1, 4)
1 on 1st die and 5 on 2nd die (1, 5)
1 on 1st die and 6 on 2nd die (1, 6)
Similarly (2, 1), (2, 2)(2, 3), (2, 4),(2, 5),(2, 6)
(3, 1), (3,2), (3,3), (3, 4), (3, 5), (3, 6)
(4,1), (4,2), (4, 3), (4,4), (4,5), (4, 6)
(5, 1), (5, 2),(5, 3), (5, 4), (5, 5), (5, 6)
(6,1), (6, 2), 6, 3), (6,4), 6, 5), (6, 6)
sample space consists of 36 outcomes.
