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Paper 1 – Evaluating Probabilities
Example
The weekly number of traffic accidents occurred in a certain road follows a Poisson distribution with mean 0.45 .
( a ) Find the probability that at least two traffic accidents will occur in this road in a particular week .
[ 2 ] ( b ) Find the probability that exactly five traffic accidents will occur in this road in a particular four-week period . [ 2 ]
( c ) Given that in a particular four-week period at most five traffic accidents occur , find the probability that less than four traffic accidents occur .
[ 3 ]
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Solution
( a ) X ~ Po ( 0.45 ) P ( X � 2 ) �1� P ( X � 1 )
( M1 ) for valid approach
P ( X � 2 ) �1�
0.9245608199 P ( X �2 ) � 0.0754391801 P ( X �2 ) � 0.0754
A1
( b ) Y ~ Po ( 1.8 ) ( M1 ) for valid approach
( c )
P ( Y �5 ) � 0.0260286241 P ( Y �5 ) � 0.0260
A1
P ( Y � 4 �Y
� 5 ) P ( Y � 4 | Y � 5 ) �
P ( Y � 5 ) P ( Y � 3 )
P ( Y � 4 | Y � 5 ) � P ( Y � 5 )
( A1 ) for substitution
0.8912916054 P ( Y � 4 | Y � 5 ) � ( A1 ) for correct approach
0.9896219631 P ( Y � 4 | Y � 5 ) � 0.9006384646
P ( Y � 4 | Y � 5 ) � 0.901
A1
[ 2 ]
[ 2 ]
[ 3 ] www . seprodstore . com
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