For each of the following, state whether the two events are complementary:
Event 1: Selecting a positive number.
Event 2: Selecting a negative number.
Event 1: Drawing a red card from a standard deck of cards (no jokers).
Event 2: Drawing a black card from a standard deck of cards (no jokers).
Event 1: Drawing a club from a standard deck of cards (no jokers).
Event 2: Drawing a spade from a standard deck of cards (no jokers).
Event 1: Rolling a number greater than 3 on a die.
Event 2: Rolling a number less than 3 on a die.
Event 1: A coin is tossed and lands on heads.
Event 2: A coin is tossed and lands on tails.
Event 1: A coin is tossed twice and lands on heads both times.
Event 2: A coin is tossed twice and lands on tails both times.
Event 1: Selecting an even non-zero integer.
Event 2: Selecting an odd non-zero integer.
Find each of the following probabilities, find the probablity that the complementary event will occur:
\dfrac{4}{5}
0.64
A biased coin is flipped, with heads and tails as possible outcomes. Calculate P \left( \text{heads} \right) if P \left( \text{tails} \right)=0.56.
The sample space of an event is listed as S = \left\{\text{short}, \text{average}, \text{tall}\right\}. If P \left( \text{average} \right)=0.5 and P \left( \text{short} \right)=0.3, find P \left( \text{tall} \right).
The probability of the local rugby team winning their grand final is 0.39. Find the probability that they won't win the grand final.
A regular die is rolled. Find the probability of:
Rolling a 1.
Not rolling a 1.
Rolling 1 or not.
Rolling either 1 or 2.
Not rolling a 4.
Not rolling a 1 or 5.
Not rolling an even number.
Not rolling an 8.
Not rolling a 1,\,2,\,3,\,4,\,5, or 6.
A number between 1 and 100 inclusive is randomly picked.
State the complement of picking a number greater than 61.
Find the probability that the number picked is greater than 61.
A bag contains 34 red marbles and 35 blue marbles. If picking a marble at random, find:
P \left( \text{red} \right)
P \left( \text{not red} \right)
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:
P \left( \text{orange} \right)
P \left( \text{orange or pink} \right)
P \left( \text{not orange} \right)
P \left( \text{neither orange nor pink} \right)
A marble is randomly drawn from a bag which contains 4 red marbles, 6 green marbles and 8 blue marbles. Find:
P\left(\text{not red}\right)
P\left(\text{red}\right) + P\left(\text{not red}\right)
P\left(\text{not green}\right)
P\left(\text{green}\right) + P\left(\text{not green}\right)
A marble is chosen at random from a box containing 4 different coloured marbles: red, blue, green and purple. The probability of selecting different colours is given in the table.
| Colour | \text{P(red)} | \text{P(blue)} | \text{P(green)} |
|---|---|---|---|
| Probability | \dfrac{2}{13} | \dfrac{2}{9} | \dfrac{1}{4} |
Find the probability of:
Not selecting a green marble.
Not selecting a blue marble.
Not selecting a purple marble.
Selecting a red or purple marble.
Selecting neither a blue or green marble.
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 K, R or T
Selecting a letter that is not in the word PROBABILITY
Not selecting a T, L, Q, A, K or Z
Selecting a letter that is not in the word WORKBOOK
A card is selected from a standard deck of cards:
Find the probability of:
Selecting a nine
Selecting a fifteen
Selecting a diamond
Selecting a spade
Selecting a red card
Selecting a black card
Selecting a face card
Selecting a black nine.
Selecting a red nine.
Selecting a yellow six
Selecting a red non-face card
Selecting an even numbered black card
Selecting an odd numbered red card
Selecting a red or black card
Not selecting a red three.
Not selecting a queen of clubs
Not selecting a red ten or black jack
Not selecting a heart
Not selecting a black card
Not selecting a black nine
Not selecting a four of hearts
Not selecting neither a red eight nor or black six
A grade of 172 students are to choose to study either Mandarin or Spanish (or both). 79 students choose Mandarin and 111 students choose Spanish.
How many students have chosen both languages?
If a student is picked at random, find the probability that the student has chosen Spanish only.
If a student is picked at random, find the probability that the student has not chosen Mandarin.