Relations and Functions
Numbers and Sequences
- Surface Area of Cylinder
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Frustum of a Cone
- Volume of a Cylinder
- Volume of a Right Circular Cone
- Volume of a Sphere
- Volume of Frustum of a Cone
- Volume and Surface Area of Combined Solids
- Conversion of Solids from One Shape to Another with No Change in Volume
Statistics and Probability
- Tree diagram
- Probability of an Event
Probability is the extent to which an event is likely to occur.
Probability is the branch of mathematics that measures the uncertainty of the occurrence of an event using numbers.
It is expressed as a fraction or percentage using the following formula.
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event, and 1 indicates certainty.
The higher the probability of an event, the more likely it is that the event will occur.
For a random experiment, if sample space is ‘S’and ‘A’ is an expected event then the probability of ‘A’ is P(A). It is given by the following formula.
P(A) = `"Number of sample points in event A"/"Number of sample points in sample spaces" = "n(A)"/"n(S)"`.
Write the sample space for selecting two balls from a bag containing 6 balls numbered 1 to 6 (using tree diagram)
If A is an event of a random experiment such that `"P"("A"):"P"(bar"A")` = 17 : 15 and n(S) = 640 then find `"P"(bar"A")`
If A is an event of a random experiment such that `"P"("A") : "P"(bar"A")` = 17 : 15 and n(S) = 640 then find n(A)
At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that the second player wins a prize if the first has won?
A bag contains 12 blue balls and x red balls. If one ball is drawn at random what is the probability that it will be a red ball?
A bag contains 12 blue balls and x red balls. If one ball is drawn at random if 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that it will be a red ball, then find x.