# 12.04 Complementary events

Worksheet
Complementary events
1

For each of the following, state whether the two events are complementary:

a

Event 1: Selecting a positive number.

Event 2: Selecting a negative number.

b

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).

c

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).

d

Event 1: Rolling a number greater than 3 on a die.

Event 2: Rolling a number less than 3 on a die.

e

Event 1: A coin is tossed and lands on heads.

Event 2: A coin is tossed and lands on tails.

f

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.

g

Event 1: Selecting an even non-zero integer.

Event 2: Selecting an odd non-zero integer.

2

Find each of the following probabilities, find the probablity that the complementary event will occur:

a

\dfrac{4}{5}

b

0.64

3

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.

4

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).

5

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.

6

A regular die is rolled. Find the probability of:

a

Rolling a 1.

b

Not rolling a 1.

c

Rolling 1 or not.

d

Rolling either 1 or 2.

e

Not rolling a 4.

f

Not rolling a 1 or 5.

g

Not rolling an even number.

h

Not rolling an 8.

i

Not rolling a 1,\,2,\,3,\,4,\,5, or 6.

7

A number between 1 and 100 inclusive is randomly picked.

a

State the complement of picking a number greater than 61.

b

Find the probability that the number picked is greater than 61.

8

A bag contains 34 red marbles and 35 blue marbles. If picking a marble at random, find:

a

P \left( \text{red} \right)

b

P \left( \text{not red} \right)

9

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:

a

P \left( \text{orange} \right)

b

P \left( \text{orange or pink} \right)

c

P \left( \text{not orange} \right)

d

P \left( \text{neither orange nor pink} \right)

10

A marble is randomly drawn from a bag which contains 4 red marbles, 6 green marbles and 8 blue marbles. Find:

a

P\left(\text{not red}\right)

b

P\left(\text{red}\right) + P\left(\text{not red}\right)

c

P\left(\text{not green}\right)

d

P\left(\text{green}\right) + P\left(\text{not green}\right)

11

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.

Find the probability of:

a

Not selecting a green marble.

b

Not selecting a blue marble.

c

Not selecting a purple marble.

d

Selecting a red or purple marble.

e

Selecting neither a blue or green marble.

12

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:

a

Not selecting a B

b

Not selecting a K, R or T

c

Selecting a letter that is not in the word PROBABILITY

d

Not selecting a T, L, Q, A, K or Z

e

Selecting a letter that is not in the word WORKBOOK

13

A card is selected from a standard deck of cards:

Find the probability of:

a

Selecting a nine

b

Selecting a fifteen

c

Selecting a diamond

d

e

Selecting a red card

f

Selecting a black card

g

Selecting a face card

h

Selecting a black nine.

i

Selecting a red nine.

j

Selecting a yellow six

k

Selecting a red non-face card

l

Selecting an even numbered black card

m

Selecting an odd numbered red card

n

Selecting a red or black card

o

Not selecting a red three.

p

Not selecting a queen of clubs

q

Not selecting a red ten or black jack

r

Not selecting a heart

s

Not selecting a black card

t

Not selecting a black nine

u

Not selecting a four of hearts

v

Not selecting neither a red eight nor or black six

14

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.

a

How many students have chosen both languages?

b

If a student is picked at random, find the probability that the student has chosen Spanish only.

c

If a student is picked at random, find the probability that the student has not chosen Mandarin.