7.5 probability II, SPM Practice (Long Questions)
Question
3:
A card is picked at random from box A and then a card is
picked at random from box B.
By listing the sample of all possible outcomes of the event,
find the probability that
(a) a card labelled M and a card with an even number are picked,
(b)
a card labelled Q or a card with a number which is multiple of 2 are picked.
Solution:
Sample
space, S
=
{(M, 2), (M, 3), (M, 6), (Q, 2), (Q, 3), (Q, 6)}
n(S) = 6
(a)
{(M, 2), (M, 6)}
$P\left(M\text{andevennumber}\right)=\frac{2}{6}=\frac{1}{3}$
(b)
{(Q, 2), (Q, 3), (Q, 6), (M, 2), (M, 6)}
$P\left(Q\text{ormultipleof2}\right)=\frac{5}{6}$
Question
4:
Table
below shows the names of participants from two secondary schools attending a public
speaking training programme.
Boys

Girls


School
A

Karim

Rosita
Sally
Linda

School
B

Ahmad
Billy

Nancy

Two
participants are required to give speeches at the end of the programme.
(a) A participant is
chosen at random from School A and
then another participant is chosen at random also from School A.
(i)
List
all the possible outcomes of the event in this sample space.
(ii)
Hence,
find the probability that a boy and a girl are chosen.
(b) A participant is
chosen at random from the boys group and then another participant is chosen at
random from the girls group.
(i)
List
all the possible outcomes of the event in this sample space.
(ii)
Hence,
find the probability that both participants chosen are from School B.
Solution:
(a)(i)
Sample
space, S
=
{(Karim, Rosita), (Karim, Sally), (Karim, Linda), (Rosita, Sally), (Rosita, Linda),
(Sally, Linda)}
n(S) = 6
(a)(ii)
{(Karim,
Rosita), (Karim, Sally), (Karim, Linda}
$P\left(\text{aboyandagirl}\right)=\frac{3}{6}=\frac{1}{2}$
(b)(i)
Sample
space, S
=
{(Karim, Rosita), (Karim, Sally), (Karim, Linda), (Karim, Nancy), (Ahmad, Rosita),
(Ahmad, Sally), (Ahmad, Linda), (Ahmad, Nancy), (Billy, Rosita), (Billy, Sally),
(Billy, Linda), (Billy, Nancy)}
n(S) = 12
(b)(ii)
{(Ahmad,
Nancy), (Billy, Nancy)}
P (both
participants from School B)
$\begin{array}{l}=\frac{2}{12}\\ =\frac{1}{6}\end{array}$