Three strangers meet on a train. Assuming that a person is equally likely to be born in any of the $12$ months of the year, find the probability that at least two of these three people were born in the same month of the year.

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Important Questions on Probability

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>END-OF-CHAPTER REVIEW EXERCISE 4>Q 19

A box contains three black and four white chess pieces. Find the probability that a random selection of five chess pieces, taken one at a time without replacement, contains exactly two black pieces which are selected one immediately after the other.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>END-OF-CHAPTER REVIEW EXERCISE 4>Q 20

The following table shows the numbers of IGCSE $(I)$ and $A$ Level $(A)$ examinations passed by a group of university students.

				IGCSEs $(I)$
		$5$	$6$	$7$	$8$	$9$	$10$
	$2$	$13$	$9$	$5$	$4$	$2$	$0$
A Levels $(A)$	$3$	$7$	$8$	$9$	$6$	$1$	$0$
	$4$	$0$	$0$	$1$	$0$	$1$	$0$
	$5$	$0$	$0$	$0$	$0$	$0$	$1$

For a student selected at random, find:

$P (I + A = 11 ∣ A < 4)$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>END-OF-CHAPTER REVIEW EXERCISE 4>Q 20

The following table shows the numbers of IGCSE $(I)$ and $A$ Level $(A)$ examinations passed by a group of university students.

				IGCSEs $(I)$
		$5$	$6$	$7$	$8$	$9$	$10$
	$2$	$13$	$9$	$5$	$4$	$2$	$0$
A Levels $(A)$	$3$	$7$	$8$	$9$	$6$	$1$	$0$
	$4$	$0$	$0$	$1$	$0$	$1$	$0$
	$5$	$0$	$0$	$0$	$0$	$0$	$1$

For a student selected at random, find:

$P (I - A > 5 ∣ I + A > 10)$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>END-OF-CHAPTER REVIEW EXERCISE 4>Q 20

The following table shows the numbers of IGCSE $(I)$ and $A$ Level $(A)$ examinations passed by a group of university students.

				IGCSEs $(I)$
		$5$	$6$	$7$	$8$	$9$	$10$
	$2$	$13$	$9$	$5$	$4$	$2$	$0$
A Levels $(A)$	$3$	$7$	$8$	$9$	$6$	$1$	$0$
	$4$	$0$	$0$	$1$	$0$	$1$	$0$
	$5$	$0$	$0$	$0$	$0$	$0$	$1$

Six students who all have at least three A Level passes are selected at random. Find the greatest possible range of the total number of IGCSE passes that they could have.