23.04 Theoretical probability
Consider this list of numbers: 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 7, 7, 7, 7, 9, 9
How many numbers are in the list?
A number is chosen from the list at random. Find the probability that it is an odd number.
State the number that has the same probability of being picked as 4.
A number is chosen from the list at random. State the number that has the highest probability of being chosen.
A number between 1 and 20 inclusive is randomly picked. Find:
The probability that the number is at least 8.
The probability that the number is less than 8.
A standard deck of 52 cards is shown below:
If a card is selected at random, find:
The probability that it is a red card.
The probability that it is a card between 5 and 9 inclusive.
The probability that it is a card that is red and has a number between 5 and 9 inclusive.
The probability that it is a card that is red or a king.
The probability that it is a spade, with a number printed on it.
The probability that it is a red card that has a number more than 2 and at most 9.
The probability that it is a black or Kings, but not both.
A spinner has 4 sectors with a star, 4 sectors with apple, and 2 sectors with an elephant. All the sectors are the same size.
Find the probability of spinning an elephant.
Find the probability of spinning an apple.
Are the two events in parts (a) and (b) mutually exclusive?
Are the two events in parts (a) and (b) complementary?
The probability that Victoria will win the major prize in a raffle at the school fete is 0.053. Find the probability that Victoria will not win.
The probability of the local football team winning their grand final is 0.36. Find the probability that they won't win the grand final.
The probability that it hails today is 0.43. Find the probability that it doesn't hail.
A biased coin is flipped, with heads and tails as possible outcomes. Calculate P(\text{heads}) if P(\text{tails})=0.56.
A company that makes sprockets guarantees that they will be within 0.5\text { mm} either way of the client's chosen size. There is a probability of 0.968 that a sprocket will be within the allowable size, find the probability that a sprocket won't be within the allowable size.
A number between 1 and 100 inclusive is randomly picked. The probability that the number is less than 61 is \dfrac{60}{100}.
What is the complement of drawing a number greater than 61?
Find the probability that the number is greater than 61.
A number between 1 and 50 inclusive is randomly picked. The probability that the number is less than 42 is \dfrac{82}{100}.
State the complement of drawing a number less than 42.
State the complement of drawing a number that is at least 43.
Find the probability that the number is at least 42.
The 26 letters of the alphabet are written on pieces of paper and placed in a bag. If one letter is picked out of the bag at random, find the probability of:
Not selecting a B.
Not selecting a C.
Not selecting a K, R or T.
Not selecting a K, L or M.
Selecting a letter that is not in the word PROBABILITY.
Not selecting a T, L, Q, A, K or Z.
Not selecting a A, E, I, O or U.
Selecting a letter that is not in the word WORKBOOK.
A letter is chosen at random from the word ORDERED.
State the letter that has the highest probability of not being chosen.
Find the probability that the chosen letter is not "D".
A standard 6-sided die is rolled once.
Find the probability of rolling a prime number.
Find the probability of rolling an odd number.
Are the two events in parts (a) and (b) mutually exclusive?
Are the two events in parts (a) and (b) complementary?
The probability of not rolling a 2.
The probability of not rolling a 2 or 5.
The probability of not rolling an odd number.
The probability of not rolling a 9.
The probability of not rolling a 1, 2, 3, 4, 5 or 6.
A bag contains red marbles and blue marbles. Given the probability of drawing a red marble is 21/44, find the probability of drawing a blue marble.
Another bag contains 34 red marbles and 35 blue marbles. If a marble is picked at random, find:
P(\text{red})
P(\text{Not Red})
A bag contains 50 black marbles, 37 orange marbles, 29 green marbles and 23 pink marbles. If a marble is selected at random, find the following probabilities, in simplest form:
P(orange)
P(orange or pink)
P(not orange)
P(neither orange nor pink)
Mario has a bag of marbles. It contains 3 white marbles and 5 marbles of other colours. Mario picks a marble from the bag without looking.
Find the probability that Mario picks a white marble.
Find the probability that Mario picks a marble that is not white.
Are the two events in parts (a) and (b) mutually exclusive?
Are the two events in parts (a) and (b) complementary?
A marble is chosen at random from a box containing 4 different colour marbles, red, blue, green and purple. The probability of selecting different colours is given in the table. Find:
The probability of not selecting a green marble.
The probability of not selecting a blue marble.
The probability of selecting a red or purple marble.
The probability of not selecting a purple marble.
The probability of selecting neither a blue or green marble.
| Colour | Probability |
|---|---|
| \text{Red} | \quad \enspace \, \dfrac{3}{13} |
| \text{Blue} | \quad \enspace \enspace \dfrac{2}{9} |
| \text{Green} | \quad \enspace \enspace \dfrac{1}{5} |
A constellation is randomly selected from the eight shown below:
Find the probability that the name of the constellation begins with a vowel.
The complementary event is selecting a constellation that begins with a consonant. Find the probability of this event.
Find the probability that the constellation has 6 or more stars.
The complementary event is selecting a constellation that has less than 6 stars. Find the probability of this event.