7.5.2 Kebarangkalian, SPM Praktis (Kertas 1)

Soalan 3:
Satu ruang sampel bagi suatu eksperimen diberi oleh S = {1, 2, 3, … , 21}. Peristiwa-peristiwa Q dan R ditakrifkan seperti berikut:
Q : {3, 6, 9, 12, 15, 18, 21}
R : {1, 3, 5, 15, 21}

Cari
(a) P(Q)
(b) P(Q dan R)

Penyelesaian:
(a)

$\begin{array}{l}n\left(S\right)=21,n\left(Q\right)=7\\ P\left(Q\right)=\frac{7}{21}=\frac{1}{3}\end{array}$

(b)
$\begin{array}{l}Q\cap R=\left\{3,15,21\right\},\\ makan\left(Q\cap R\right)=3\\ P\left(Q\text{ dan }R\right)=P\left(Q\cap R\right)\\ =\frac{n\left(Q\cap R\right)}{n\left(S\right)}\\ =\frac{3}{21}\\ =\frac{1}{7}\end{array}$

Soalan 4:
Peristiwa A dan B adalah bersandar.
$\begin{array}{l}\text{Diberi }P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{1}{4}\text{ dan }P\left(A\cup B\right)=\frac{1}{5},\text{ cari}\\ \text{(a) }P\left[\left(A\cup B\right)\text{'}\right],\\ \text{(b) }P\left(A\cap B\right).\end{array}$

Penyelesaian:
(a)
$\begin{array}{l}P\left[\left(A\cup B\right)\text{'}\right]=1-P\left(A\cup B\right)\\ =1-\frac{1}{5}\\ =\frac{4}{5}\end{array}$

(b)
$\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cup B\right)\\ =\frac{3}{5}+\frac{1}{4}-\frac{1}{5}\\ =\frac{13}{20}\end{array}$