BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles
Binôme : Anglais / Mathématiques Sujet n° 15 STATISTICS/PROBABILITY The first part of this page is a summary that can be helpful to do the exercise. PROBABILITY: remember the following rules. P(an event does not occur) = 1 – P(the event does occur). For two events A and B, P(A or B) = P(A) + P(B) – P(A and B) , where “A or B” means “A or B or both”. Two events, A and B, are independent if the outcome of one event does not affect the outcome of the other, in which case P(A and B) = P(A) × P(B). P(B|A) represents the probability of event B occurring given that A has occurred: P(B|A)=
P( A ∩ B) . P ( A)
AVERAGES: The mode of a set of values is the value which occurs most frequently. The modal class of a grouped frequency distribution is the class with the greatest frequency. The arithmetic mean of the values x1, x2, …., xp whose corresponding frequencies are n1, n2, …., np, is x = n1x1+n2x2+….+npxp . n1+n2+….+np For a grouped frequency distribution (continuous or discrete), the numbers x1, x2, ….., xn are the class mid-values. The median is the value of the variable which stands in the middle of the distribution when the values are arranged in order of size.
EXERCISE : Mark Number of students
1 1
2 2
3 4
4 7
5 4
6 8
7 2
The table shows the marks obtained by 28 students in a history test. (i)
Write down the mode.
(ii)
Find the median.
(iii)
Calculate the mean.
(iv)
Two students are chosen at random. Calculate the probability that they both obtained mark 5.
(v)
Among all the students who obtained 4 or 5 or 6 or 7, two are chosen at random. Calculate the probability that they both obtained mark 5.
(vi)
Among the original 28, students are chosen at random, one after the other, until we pick one with mark 5. Calculate the probability that he is the third student chosen. Adapted from IGCSE exam, Cambridge University, 2001
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