 ## Dependent Events and Independent Events

 9.2 Dependent Events and Independent Events

• Combined events can be categorised as dependent and independent events

 Event $$A$$ and event $$B$$ are independent events if the occurrence of event $$A$$ has no effecrt on the occurrence of event $$B$$ and vice versa

• In other words, event $$A$$ and event $$B$$ are dependent events if the occurrence of event $$A$$ affects the occurrence of event $$B$$.

 Example Identify whether the following combined events are dependent events or independent events.  Justify your answers. 1. Taking an Uber ride and getting a free meal at your favourite restaurant Solution: It is an independent events because the probability of taking an uber does not affetct the probability of getting a free meal at favourite restaurant. 2. Getting into a traffic accident is dependent upon driving or riding in a vehicle. Solution: It is a dependent event because the probability of getting into a traffic accident has affect driving or riding in a vehicle

Verify conjecture and verify about the formu;a of probability of combined events .

 The probability of the intersection of two intersection events $$A$$ and $$B$$ is equal to the product of the probability of event $$A$$ and probability of event $$B$$

• In general, $$P(A \space \text{and} \space B) = P(A) \times P(B)$$

 Example Khairil has $$40$$ cards consisting of white, blue and red. If a card is chosen at random, the probability of choosing a red card is $$\dfrac{3}{5}$$. Calculate a)  number of cards in red. b) the probability of choosing a blue card if Khairil has $$8$$ white cards. Solution: If:  \begin{aligned}P &= \text{White card event selected.}\\ B &= \text{Blue card event selected.}\\ M &= \text{Red card event selected.}\\ S &= \text{Sample space}\end{aligned} a)   \begin{aligned}n(S) &= 40\\ n(M)&=P(M)\times n(S)\\&=\dfrac{3}{5}\times40\\&=24.\end{aligned}   b) \begin{aligned}\text{Give,} \\\,\\n(P) &= 8\\ n(B) &= 40 – 24 – 8 = 8\\\,\\ P(B)&=\dfrac{n(B)}{n(S)}\\&=\dfrac{8}{40}\\&=\dfrac{1}{5}. \end{aligned}