Probability – Formula & Equation Sheet
Essential formulas and equations from Mathematic, tailored for Class 10 in Mathematics.
This one-pager compiles key formulas and equations from the Probability chapter of Mathematic. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
P(E) = \frac{Number \ of \ outcomes \ favourable \ to \ E}{Total \ number \ of \ possible \ outcomes}
P(E) defines the theoretical probability of an event E occurring. Represents ratio of favorable outcomes to total possible outcomes in an experiment.
P(not E) = 1 - P(E)
Calculates the probability of the complement of event E. Ensures that the sum of probabilities of an event and its complement equals 1.
P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2)
This is the addition rule for probabilities of two events E1 and E2. Useful for calculating the probability of either event occurring.
P(E_1 \cap E_2) = P(E_1) \times P(E_2) \ (if \ E_1, E_2 \ are \ independent)
Defines the probability of both events E1 and E2 occurring together, applicable when events are independent.
P(E) + P(not E) = 1
This identity reflects that the total probability for all outcomes in an experiment equals one, reinforcing the concept of complementary events.
P(E_1 \cup E_2 \cup E_3) = P(E_1) + P(E_2) + P(E_3) - P(E_1 \cap E_2) - P(E_1 \cap E_3) - P(E_2 \cap E_3) + P(E_1 \cap E_2 \cap E_3)
This is an extension for three events and is useful when finding the cumulative probability of multiple events.
P(E) = 0 \ (impossible \ event)
Indicates situations where an event cannot occur, such as drawing a number greater than 6 from a die.
P(E) = 1 \ (certain \ event)
Represents a situation that will definitely occur, e.g., rolling a number less than 7 on a die.
If \ n \ is \ the \ total \ number \ of \ marbles, \ P(red) = \frac{n_{red}}{n}
For a bag of different colored marbles, this formula calculates the probability of drawing a red marble.
Outcomes \ of \ a \ die:\ {1, 2, 3, 4, 5, 6}
Sets the foundation for calculating probabilities related to any event regarding the die's throw.
Equations
P(E) = \frac{number \ of \ favourable \ outcomes}{total \ number \ of \ outcomes}
Fundamental equation for calculating any event's probability. Example: Tossing a coin to get heads.
P(Head) = \frac{1}{2}
The probability of getting heads when a fair coin is tossed once.
P(Tail) = \frac{1}{2}
The probability of getting tails when a fair coin is tossed once.
P(Yellow \ ball) = \frac{1}{3}
The probability of drawing a yellow ball from a bag containing red, blue, and yellow balls.
P(\text{sum}=8 \ in \ two \ dice) = \frac{5}{36}
Probability of obtaining a sum of 8 when rolling two six-sided dice.
P(\text{sum}>12) = 0
No outcomes yield a sum greater than 12 when throwing two dice.
P(\text{sum}\leq12) = 1
All possible outcomes of two dice rolls result in a sum of 12 or less.
P(Boy) = \frac{1}{2}
The probability of a newborn being a boy, assuming equal likelihood for boys and girls.
P(Girl) = \frac{1}{2}
The probability of a newborn being a girl, assuming equal likelihood for boys and girls.
From \ n = 6, \ P(rolling \ a \ 4) = \frac{1}{6}
Finding the probability of rolling a 4 on a standard die with 6 faces.
