Analysis and Approaches for IBDP Maths Ebook 2 | Page 235

73
Paper 1 Section A – Geometric Series Problems
Example
Two players, A and B , alternately throw a fair six-sided dice, with A starting, until one
of them obtains a three.
(a)
(b)
Find the probability that A obtains the first three in one of his first two turns.
Find the probability that A obtains the first three.
[3]
[4]
Solution
(a)
(b)
The required probability
1 � 5 �� 5 �� 1 �
� � � �� �� �
M1A1
6 � 6 �� 6 �� 6 �
1 25
� �
6 216
36 25
� �
216 216
61
� A1
216
The required probability
[3]
17
1 � 5 �� 5 �� 1 � �� 5 �� 5 ��
� 1 �
� � � �� �� � � �� �� ��
� � �
6 � 6 �� 6 �� 6 � �� 6 �� 6 ��
� 6 �
2
M1A1
2
1 � 25 �25
�
� 1� � �
6 � � �
�
36 �36
�
�
�
�
� �
1�
1 �
� �
6 25
�
� 1 � �
� 36 �
A1
1 �36
�
� � �
6 �11
�
6
� A1
11
[4]
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