12.03 Theoretical probability
Yuri has 5 blue marbles, 1 red marble, 1 yellow marble and 1 black marble in a bag. Yuri picks a marble from the bag without looking. Find the probability that Yuri picks a blue marble.
A bag contains 21 red marbles and 26 blue marbles. Find the probability of drawing a red marble.
A bag contains 49 marbles. 24 of them are red and the rest are of them are blue. Find the probability of drawing a blue marble.
A spinner has ten sectors of the same size:
5 of the sectors show a star.
2 of the sectors show an apple.
3 of the sectors show an elephant.
Find the probability of spinning an elephant.
A letter is chosen at random from the word COCOONS.
Which letter is most likely to be chosen?
Find the probability that the chosen letter is a "C".
The numbers from 2 to 10 are written on separate cards. One card is chosen at random. Find the probability that the number is:
A multiple of 2.
A prime number.
A number less than 6.
A two-digit number is formed only using the digits 3 and/or 2.
List all the possible two-digit numbers.
Find the probability that the number formed is odd.
Find the probability that the number formed is more than 30.
A three-digit number is formed only using the digits 2, 7, and/or 8. Some of the possible three-digit numbers are listed below:
222, \enspace 227, \enspace 228, \enspace 272, \enspace 277, \enspace 278, \enspace 282, \enspace 287, \enspace 288, \\ 722, \enspace 727, \enspace 728, \enspace 772, \enspace 777, \enspace 778, \enspace 782, \enspace 787, \enspace 788List the remaining possible three-digit numbers.
Find the probability that the number formed is odd.
Find the probability that the number formed is palandromic (the same forwards as backwards).
A full set of scrabble tiles is shown in the diagram below. The last two letters are the two "blank" tiles:
| A | A | A | A | A | A | A | A | A | B |
| B | C | C | D | D | D | D | E | E | E |
| E | E | E | E | E | E | E | E | E | F |
| F | G | G | G | H | H | I | I | I | I |
| I | I | I | I | I | J | K | L | L | L |
| L | M | M | N | N | N | N | N | N | O |
| O | O | O | O | O | O | O | P | P | Q |
| R | R | R | R | R | R | S | S | S | S |
| T | T | T | T | T | T | U | U | U | U |
| V | V | W | W | X | Y | Y | Z |
One letter tile is drawn at random:
Find the probability that it is a "G" or an "R".
Find the probability of drawing a vowel.
Luigi and Danielle enter a raffle where 80 tickets are on sale. Luigi buys 1 ticket and Danielle buys 5 tickets.
Find the probability that Luigi wins if all the tickets were sold.
Find the probability that Danielle wins if all the tickets were sold.
Find the probability that Danielle wins if only 70 tickets were sold.
Consider the following dice:
Four-sided die
Six-sided die
Eight-sided die
Ten-sided die
Twelve-sided die
Twenty-sided die
State the die that would give the highest probability of rolling the following:
16
1
9
Neil takes the following cards and shuffles them up. He draws one card, shows it to you, and keeps it. You then draw one card from the remaining seven cards, and you win if the number on your card is higher than Neil's.
Find your chance of winning if Neil draws the following cards:
A bag contains 28 red marbles, 27 blue marbles, and 26 black marbles.
Find the probability of drawing a blue marble.
A single trial is drawing a marble from the bag, writing down the colour, and putting it back. If this trial is repeated 400 times, how many blue marbles should you expect? Round your answer to the nearest whole number.
A die is rolled 358 times.
If it lands on a six 12 times, what is the probability that the next roll will land on a six?
Does the outcome of the next roll depend on the outcome of previous rolls?
This spinner is spun 12 times. Find the number of times we would expect to spin:
An apple.
A ball.
If the probability of an event is \dfrac{2}{3}, how many times would you expect the event to occur in 18 trials?
A six-sided die is rolled 24 times. How many times should we expect to roll a 1?
An eight-sided die is rolled 24 times. How many times should we expect to roll a 7? Round your answer to the nearest whole number.
A twenty-sided die is rolled 100 times. How many times should we expect to roll a 14 or more? Round your answer to the nearest whole number.