7.05 Mutually exclusive events
Two events A and B are mutually exclusive.
If P(A) = 0.37 and P(A\text{ } \text{or}\text{ } B) = 0.73, find P(B).
If P(A) = 0.8, P(B) = 0.75 and P(A\text{ } \text{and} \text{ } B)= 0.6, find P(A\text{ } \text{or}\text{ } B).
A card is drawn at random from a standard deck. Find the probability that the card is:
A king or a 3.
A spade or a diamond.
An ace of spades or an ace of clubs.
A ten, jack, queen, king or an ace.
An ace of spades or a king of hearts.
A red or a diamond.
An ace or a diamond.
A black or a face card.
Not a red ten or black jack.
A bag contains 86 marbles, some of which are black and some of which are white. If the probability of selecting a black marble is \dfrac{33}{43}, find:
The number of black marbles in the bag.
The number of white marbles in the bag.
Consider the following formula: n\left(A \cup B\right) = n\left(A\right) + n\left(B\right) - n\left(A \cap B\right).
Translate the formula in words.
Does the formula hold for the sets A and B shown in the Venn diagram?
Does the formula hold for the sets \\A = \left\{2, 4, 5, 6, 8, 9\right\} and \\B = \left\{0, 1, 3, 4, 5, 7, 10\right\}?
Use the Venn diagram to explain why we must subtract n\left(A \cap B\right).
A standard six-sided dice is rolled. Find the probability of rolling:
The number 4.
An odd number.
A 4 or an odd number.
An even or prime number.
A number that is even and prime.
An even number or a factor of 6.
A factor of 9 or an even number.
A number less than 3.
A number greater than 5.
a number less than 3 or greater than 5.
For each of the following probability Venn diagrams:
Calculate the value of x in the diagram.
State whether A and B are mutually exclusive.
The results from a recent survey showed that 79 people speak Spanish or French. Of these, 49 speak Spanish, and 18 speak both Spanish and French.
Find the number of people surveyed who speak French.
The result of a recent survey showed that 34 people own a dog, 33 own a cat, and 13 own both a dog and a cat.
How many people surveyed own at least one dog or cat?
The number of movie, concert and music tickets on offer as a prize are in the ratio 8:19:3.
Find the probability that the winner will be given a concert ticket.
The winner doesn’t want to see a musical. Find the probability that they get a ticket they do want.
A circular spinner is divided into unequal parts. The green sector takes up an angle of 250 degrees at the centre. The red sector takes up an angle of 60 degrees at the centre and the blue sector takes up the remainder of the spinner.
Find the probability that the spinner will land on blue.
While discussing dominant physical traits, some students completed a survey of their eye colour. Each student nominated one colour, and the results are shown in the table:
What percentage of students had hazel eyes?
Find the least number of students that could have completed the survey.
| Brown | Blue | Green | Hazel |
|---|---|---|---|
| 70\% | 15\% | 2\% |
The Venn diagram shows the decisions of 448 workers choosing to work and workers choosing to strike on a particular day of industrial action.
Find the probability that a worker selected randomly chose to:
Strike
Strike and work
Work and not strike
Work or strike
Among a group of 63 students, 12 students are studying philosophy, 48 students are studying science, and 7 students are studying neither subject.
How many students are studying philosophy and science?
If a student is picked at random, find the probability that they study at least one of these subjects.
Find the probability that a randomly selected student studies only one of the subjects.
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.