2019 Nov P1 Q11

Question 10

In a certain country,

10

-digit telephone numbers with the following format were introduced:

Digits may be repeated.

10.1

How many possible

10

-digit telephone numbers could be formed?

(2)

10.2

Certain restrictions were placed on the groups of digits:

Area code: must be $3$ digits and the first digit can NOT be $0$ or $1$
Exchange code: must be $3$ digits and the first and second digits can NOT be $0$ or $1$
Number: must be $4$ digits and the first digit MUST be a $0$ or $1$

\quad 10.2.1

How many valid

10

-digit telephone numbers could be formed by applying the given restrictions?

(3)

\quad 10.2.2

Determine the probability that any randomly chosen

10

-digit telephone number would be a valid phone number.

(2)

\textbf{[7]}

Question 11

$11.1$	Events $A$ and $B$ are independent. $P(A)=0,4$ and $P(B)=0,25$ .
$\quad 11.1.1$	Represent the given information on a Venn diagram. Indicate on the Venn diagram the probabilities associated with each region.	$(3)$
$\quad 11.1.2$	Determine $P(A\; or\; NOT\; B)$ .	$(2)$
$11.2$	Motors Incorporated manufacture cars with $5$ different body styles, $4$ different interior colours and $6$ different exterior colours, as indicated in the table below.

	The interior colour of the car must NOT be the same as the exterior colour. Motors Incorporated wants to display one of each possible variation of its car in their showroom. The showroom has a floor space of $500\, m^2$ and each car requires a floor space of $5\, m^2$ .
	Is this display possible? Justify your answer with the necessary calculations.	$(6)$
		$\textbf{[11]}$

In a certain country, $10$ -digit telephone numbers with the following format were introduced:

Digits may be repeated.
$10.1$	How many possible $10$ -digit telephone numbers could be formed?	$(2)$
$10.2$	Certain restrictions were placed on the groups of digits: Area code: must be $3$ digits and the first digit can NOT be $0$ or $1$ Exchange code: must be $3$ digits and the first and second digits can NOT be $0$ or $1$ Number: must be $4$ digits and the first digit MUST be a $0$ or $1$
$\quad 10.2.1$	How many valid $10$ -digit telephone numbers could be formed by applying the given restrictions?	$(3)$
$\quad 10.2.2$	Determine the probability that any randomly chosen $10$ -digit telephone number would be a valid phone number.	$(2)$
		$\textbf{[7]}$