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Class 10 Maths Formulas

CHAPTER 15 – PROBABILITY
1.	Probability is the likelihood of occurrence of an event.
2.	Probability of an event $$A$$ is denoted by $$P(A)$$ $$P(A)=\frac{\text{No. of favourable outcomes}}{\text{Total possible outcomes}}$$ $$=\frac{n(A)}{n(S)}$$ where $$S$$ is the sample space.
3.	Tossing a Coin (A) One toss: $$S=\{H,T\},\; n(S)=2$$ (B) Two tosses / two coins once: $$S=\{(H,H),(H,T),(T,H),(T,T)\}$$ $$n(S)=2^2=4$$ (C) Three tosses / three coins once: $$S=\{(H,H,H),(H,H,T),$$ $$(H,T,H),(H,T,T),$$ $$(T,H,H),(T,H,T),$$ $$(T,T,H),(T,T,T)\}$$ $$n(S)=2^3=8$$ In general: $$n(S)=2^n$$
4.	Throwing a Die (A) One throw: $$S=\{1,2,3,4,5,6\},\; n(S)=6$$ (B) Two dice once / one die twice: $$n(S)=6^2=36$$ (C) Three dice once / one die thrice: $$n(S)=6^3=216$$
5.	Playing Cards Total cards = 52 Red cards = 26 Black cards = 26 Cards in each suit = 13 Face cards = 12
6.	$$P(A’)$$ is the probability of event $$A$$ not happening.
7.	$$P(A)+P(A’)=1$$ $$P(A)=1-P(A’)$$ $$A$$ and $$A’$$ are complementary events.
8.	Probability of a sure event = 1
9.	Probability of an impossible event = 0
10.	$$0 \leq P \leq 1$$
11.	The sum of probabilities of all outcomes of an experiment is 1.
12.	At least means $$\geq$$ (greater than or equal to).
13.	At most means $$\leq$$ (less than or equal to).
14.	Difference between “OR” and “AND” Example: Numbers from 1 to 20 (i) Divisible by 2 or 3: Count multiples of 2 and 3, subtract multiples of 6. (ii) Divisible by 2 and 3: Count multiples of 6 only.