Identify whether the following combined events are dependent events or independent events. 

Justify your answers.

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. 

Solution:

• It is a dependent event because the probability of getting into a traffic accident has affect driving or riding in a vehicle

 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)

\(\begin{aligned}\text{Give,} \\\,\\n(P) &= 8\\ n(B) &= 40 – 24 – 8 = 8\\\,\\ P(B)&=\dfrac{n(B)}{n(S)}\\&=\dfrac{8}{40}\\&=\dfrac{1}{5}. \end{aligned}\)