Maths Quest Maths A Year 12 for Queensland Chapter 9 Probability and the binomial distribution WorkSHEET 9.2 1
WorkSHEET 9.2 Probability and the binomial distribution
Name: ______
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1 / In a class of 25 students, 11 study History and 12 study Geography. There are 5 students who study both History and Geography. Draw a Venn diagram showing the distribution of the students in these subjects. /11 study History and 5 study History and Geography
6 study History only.
12 study Geography and 5 study History and Geography
7 study Geography only.
There are 25 students in total. So, the number who study neither of these subjects
= 25 – (6 + 5 + 7)
= 7 / 6
2 / In a group of 100 students, it was found that 40 study Maths A, 30 study Drama and 54 study neither.
(a) Draw a Venn diagram to display this information.
(b) If a student is chosen at random, what is the probability that this student studies Drama but not Maths A? / (a)
/ 6
3 / A survey of a class of 30 students found that 12 owned a dog, 10 owned a cat and 16 owned neither. How many students had both a cat and a dog? /
/ 4
4 / A survey of the reading habits of 500 people found that:
130 read magazines
180 read non-fiction
220 read novels
40 read magazines and novels
20 read magazines and non-fiction
30 read novels and non-fiction
5 read all three
How many read none of these? /
500 - (135 + 15 + 5 + 25 + 75 + 35 + 155)
= 55 read none of these. / 4
5 / In a class it was found that 64% of the students like apples, 48% like bananas and 21% like both.
(a) Draw a Venn diagram showing the student preference.
(b) Find the probability that a student chosen at random is one who likes neither apples nor bananas. / 6
(a)
(b) P(likes neither apples nor bananas) = 0.09
6 / A survey of students in a class revealed that, in the year to date, 56% of the students had been on a holiday within Australia, 37% had been on an overseas holiday and 26% had been on both.
Use the Addition Rule for Probability to determine the probability that a student chosen at random had either been on an Australian or overseas holiday. / 3
7 / Write Pascal’s triangle to row 5. / / 6
8 / Use Pascal’s triangle to determine the probability of tossing 3 tails in 4 tosses of a coin. / / 5
9 / If the coin in question 8 was biased so that it landed tail up 70% of the time, what would be the probability of getting at least one tail in the four tosses. / / 5
10 / Use the Binomial Cumulative Distribution Tables in your textbook to answer the following question.
In a multiple-choice test of 20 questions there are 5 options: A, B, C, D or E. Through purely guessing, what is the probability of passing the test? / Use the Binomial Cumulative Distribution Tables on pages 455–56.
So the probability of passing by purely guessing = 0.0026. / 5