MA22S6 Numerical and Data Analysis1 2015-2016
Homework sheet 1
Due Thursday 4th of February in class
Justify your answers by a few words, in particular when using a formula.
1. We flip three coins
a) Give two possible sample spaces.
b) We define the events Ai corresponding to “exactly i tails landed”. Find the
corresponding probabilities P (Ai ).
c) What is the probability that the second coin landed tails, given that two coins
(exactly) landed head ?
d) We define the event E as being “at least one coin landed head”. Partition
the sample space according to the numbers of tails obtained and use this
partition to write P (E) in function of P (Ai ). Illustrate your result with a
Venn diagram.
2. Answer one of these two following questions
a) When plants are exposed to a certain chemical, nine out of ten are killed. In
the same time, one in ten would die naturally. In an accident, one in 100
plants in a field are exposed to the chemical. If a particular sample plant has
died, what is the probability it was exposed to the chemical?
b) An oil-prospector wishes to find out if an area has oil under the ground or
not. His instruments indicate oil is present when in actual fact it is not 10%
of the time, and that oil is absent 5% of the time when in actual fact it is
present. The probability of an area having oil under the ground is 2%. What
is the probability that an area has oil given that the test says it does not?
3. A Jar contains 3 red and 5 black balls. What is the probability of drawing
a) 2 red balls simultaneously ?
b) 3 red balls in successive draws with replacement after each draw ?
c) 3 red balls in successive draws without replacement ?
d) 2 reds and a black in a single draw of 3 balls ?
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Lecturer: Stefan Sint, sint@maths.tcd.ie, see also http://www.maths.tcd.ie/~sint/MA22S6/MA22S6.html
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