MID-TERM EXAM
COURSE: PROBABILITY AND STATISTICS
DURATION: 75 minutes
TEST 1 (Ca 3)
1. Suppose that P(A|B) = 0.4 and P(A) = 0.3; P(B) = 0.5. Determine P(AโฉB);
(A . )
P B
; P(A + B) and P(B|A).
2. A survey of all households in the town of Bury was carried out. The survey showed that
65% have a freezer and 25% have a dishwasher and 20% have neither freezer nor
dishwasher. Find the probability a chosen household has:
a) Both appliances; b) only one appliance; c) a dishwasher given that this household had a
freezer.
3. In a box there are 6 good products and 4 bad products. The first time took out 2
products, the second time also took out 2 products (without replacement).
Find the probability of getting exactly 1 good product at each time.
4. In a factory, machines A, B, and C produce electronic components. Machine A produces
25% of the components, machine B produces 60% of the components and machine C
produces the rest. Some of the components are defective. Machine A produces 4%,
machine B 3% and machine C 7% defective components.
a) Draw a tree diagram to represent this information.
Find the probability that a randomly selected component is:
b) Produced by machine A and is NOT defective.
c) Defective.
d) Given that a randomly selected component is defective, find the probability that it
was produced by machine A.
5. A box has 5 red marbles and 10 black marbles. An takes 3 marbles at random from the
box. Let X be the number of red marbles taken. Draw up the probability distribution
table for X. Find E(X) and Var(X).
6. Given ๐~ ๐ต(30; 0.6) and ๐~๐(50 ; 4๏ถ). Determine:
a) ๐(๐ < 20); ๐ (๐ > 25); ๐(46 < ๐ < 52)
b) y such that ๐(๐ > ๐ฆ)= 0.22.
7. The fish in a lake have weights that are normally distributed with a mean of 1.3 kg
and a standard deviation of 0.2 kg. Know that 15% of the fish weigh more than a. Find the value
of a.