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Probability - Independence of sets.
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Remember that if two sets A and B are independent, then P(A∩B) = P(A) P(B).
This relationship is referred to as the MULTIPLICATION LAW.
It is the same concept as two events happening sequentially with replacement.

	1. Which of the following events would be independent? (i) Throwing a 3 with a dice and selecting a King from a deck of cards. (ii) Catching a fish and wearing a lucky T-shirt. (iii) Watching your favourite team win and sitting in a lucky seat. (iv) Studying for a Maths test and obtaining a good result.
	2.
	3. The chances of developing symptoms from a trial medication for head trauma are: 10% of developing a headache and becoming dizzy; 25% of developing a headache only; 60% of becoming dizzy only. (i) Draw a 2 × 2 table to summarise this information and then compete the entries. (ii) Are the two outcomes of headache (H) and dizziness (D) independent?
	4. A and B are independent events. It is known that P(A) = 2P(B) and that P(A∪B) = 0.52. Find the probability P(A). Answer.P(A) = 0.4.
	5. For events A and B, P(A∩B) = p, P(A'∩B) = p - 1/8 and P(A∩B') = 3p/5. If A and B are independent, determine the value of p.
	7. Amongst the Year 12 girl students in my school, 12 play netball only, 5 play football only and B girls play both netball and football. The other 3 girls do not play sport. Show that, for these girls, playing netball and playing football are independent sports.
Advanced questions.	A local supermarket was reviewing its operations. It wanted to improve its customer relations and, as part of that review, decided to determine when customers were most likely to visit the store on weekdays or weekends; and whether the customers came in before 5 pm or after 5 p.m. The researcher developed the following table:   Weekday Weekend   Before 5 pm 7%   48% After 5 pm         27%   100% Three percentages from the review are entered into the above table together with the total percentage or respondents. (i) Complete the percentage entries in the table. (ii) By converting the percentages to probabilities, evaluate the conclusion that time of shopping and day of the week are independent events.