Download F78SC STATISTICS FOR SCIENCE D I Sales TUTORIAL 4 1. A fair

F78SC
STATISTICS FOR SCIENCE
D I Sales
TUTORIAL 4
1. A fair coin is tossed three times. Find the probability of getting:
(a) 3 heads; (b) 2 heads and 1 tail; (c) at least 1 tail.
2. Rainfall data was collected in Edinburgh over a three year period and days classified
as Dry or Wet (≥ 1 mm rain). The table gives the results for the 1094 possible pairs
of two consecutive days.
Pair Type
Frequency
DD
473
DW
177
WD
178
WW
266
Total
1094
Estimate the probability of a wet day in Edinburgh. Estimate the probability of a wet
day in Edinburgh, given that the previous day was dry.
3. A gambler has a biased die. The probability of it coming up 6 is a half; the other
outcomes are equally likely, so the probability distribution is:
1
x
Pr(x) 0.1
2
0.1
3
0.1
4
0.1
5
0.1
6
0.5
Calculate the mean, µ, and the standard deviation, σ, of the distribution.
If the die is thrown once, what is the probability that it shows 4, given that the value
is less than 5?
If the die is thrown twice, what is the probability that the total is 11?
4. How many times should a fair coin be tossed in order that the probability of observing
at least one head is greater than 0.95?
5. A large quantity of flower seeds are mixed together in the ratio of 2 seeds for plants
with red flowers to 3 seeds for plants with yellow flowers. They are sown with 5 seeds
per pot. Assuming that all the seeds germinate, what is the probability that a pot:
(a) contains all red flowers?
(b) contains all yellow flowers
(c) contains both red and yellow flowers?
(d) contains exactly two red flowers?
6. A test consists of 12 multiple choice questions, each with five candidate answers.
A student guesses the answers for all of the questions. What is the distribution of
X, the number of questions correct?
Find the probability of getting: (a) exactly 2 correct; (b) at least 6 correct.