Download Probability Quiz

PROBABILITY QUIZ
How good are You in
Probability?
Q1
The letters of the word GIGGS are
arranged in a line. If an
arrangement is chosen at random,
what is the probability that the
three Gs are together?
Q2
A box contains 36 marbles. If a marble is picked
at random, the probability of being red is 2/9.
How many red marbles should be added to
make this probability 1/3?
Q3
An identity card whose non-zero number is
seven digits long, each being a number from
the list {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, is picked at
random. What is the probability that the sum
of the last two digits of its number is 9?
Q4
One of the 5 points (3, 2), (2, 1), (1, –4), (5, 5)
and (4, 6) is selected at random. What is the
probability that it lies on the straight line 3x
– 2y = 5?
Q5
The letters of the word “PROBABILITY” are
written on cards and the cards are then
shuffled. If a card is picked at random, find the
probability that it will contain a vowel.
Q6
I have two 10-cent coins, three 20-cent cons,
four 50-cent coins and five $1 coins in my
pocket. If I choose a coin at random, find the
probability that the coin is worth at least 50
cents.
Q7
A man tosses two fair dice. One is numbered
1 to 6 in the usual way and the other is
numbered 1, 3, 5, 7, 9 and 11. Find the
probability that the total of the two numbers
shown is greater than 10.
Q8
A card is drawn at random from a normal pack
of 52 cards. If A represents the event that the
card drawn is a Queen and B represents the
event that the card drawn is a Heart. Find P(A
 B).
Q9
A computer produces a 4-digit random number
in the range 0000 to 9999 inclusive in such a
way that all such numbers are equally likely to
occur. Find the probability that the computer
produced a random number that begins and
ends with the digit 1.
Q10
Two fair dice, one red and one blue, are
tossed. What is the probability that the total
of the numbers shown by the two dice
exceeds 3.
Q11
A box contains 30 balls. The balls are numbered
1, 2, 3, 4, …, 30. A ball is drawn at random. Find
the probability that the number on the ball is a
prime number.
Q12
An interview with 18 people revealed that 5 of
the 8 women and 8 of the 10 men preferred
drinking coffee to tea. What is the probability
that if one person is selected from the group of
18 people, it is either a woman or someone
who preferred to drink coffee than tea.
Q13
A coin is biased in such a way that in the long
run, on the average, a head turns up 3 times
in 10 tosses. If this biased coin is tossed
simultaneously with an unbiased coin, what
is the probability that both will fall as heads?
Q14
For events A and B, P(A) = 0.5, P(B) = 0.7 and
P(A  B) = 0.85. Determine whether events A
and B are independent, mutually exclusive or
neither of these.
Q15
Ah Teck has three 50-cent coins and two 10cent coins in his pocket. He takes coins out of
his pocket, at random, one after the other. The
coins are not replaced. Find the probability that
the total value of the first three coins taken out
is 70 cents.
Q16
A bag contains 4 white chips and 3 blue chips. One chip is
drawn at random. If it is blue, it is replaced in the bag. If it is
white, it is not replaced. A second chip is then drawn from
the bag. Write down the missing probability.
First Chip
(
4/7
3/7
)
Second Chip
white
white
3/6
blue
4/7
white
3/7
blue
blue
Q17
Ten balls numbered 1 to 10 are in a jar. Andy
reaches into the jar and removes one of the
balls. Then Bernard removes another ball.
What is the probability that the sum of the two
numbers on the balls removed is even?
Q18
A particular warning system consists of two
independent alarms having chances of
operating in an emergency of 0.98 and 0.96
respectively. Find, leaving your answers in
decimals, (a) the probability that exactly one
alarm operates in an emergency, (b) the
probability that at least one alarm operates in
an emergency.
Q19
When three NPCC cadets participate in a
shooting contest, their respective
probabilities of hitting the target are 1/3, ¼
and 1/5. Calculate the probability that
exactly one bullet will hit the target if all
cadets fire at it simultaneously. Leave your
answer in fraction.