PROBABILITY QUIZHow 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 10-cent 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 Second Chip ( ) white4/7 white

3/6 blue

4/7 white3/7 blue

3/7 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.