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CHAPTER 15
PROBABILITY
1. Probability is the likelihood of occurrence of an event.
2. Probability of an event A is denoted by P ( A ) .
𝑃(𝐴) =
𝑁𝑜.𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑁𝑜.𝑜𝑓 𝑎𝑙𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 =
𝑛(𝐴)
𝑛(𝑆) S is called the sample space.
3. TOSSING A COIN :
A ) When a coin is tossed once, 𝑆 = {𝐻 , 𝑇}
𝑛( 𝑆 ) = 2
B ) When one coin is tossed twice or 2 coins are tossed once,
𝑆 = {( 𝐻, 𝐻 ), ( 𝐻, 𝑇 ), ( 𝑇, 𝐻 ), (𝑇, 𝑇)} 𝑛 ( 𝑆 ) = 22 = 4
C ) When one coin is tossed thrice or 3 coins are tossed once,
𝑆 = {( 𝐻,𝐻,𝐻 ), (𝐻,𝐻,𝑇), (𝐻,T,𝐻 ), (𝐻,𝑇,𝑇), ( 𝑇,𝐻,𝐻), (𝑇,𝐻,𝑇), (𝑇,𝑇,𝐻), 𝑇, 𝑇, 𝑇)}
𝑛(𝑆) = 23 = 8.
In general if one coin is tossed ‘n’ times or ‘n’ coins are tossed once , 𝑛(𝑆) = 2𝑛
4. THROWING A DIE :
A ) When a die is thrown once, 𝑆 = {1, 2, 3, 4, 5, 6 } 𝑛 (𝑆) = 6
B ) When a pair of dice are thrown once or a die is thrown twice
𝑆 =
{
(1,1), (1,2), − − −(1,6)
(2,1), (2,2), − − −(2,6)
(3,1), (3,2), − − −(3,6)
(4,1), (4,2) − − − (4,6)
(5,1), (5,2), − − −(5,6)
(6,1), (6,2), − − −(6,6)
𝑛(𝑆) = 62 = 36
C ) When three dice are thrown once or one die is thrown thrice
𝑛(𝑆) = 63 =216.
5. Playing Cards :
EXPHUB