 Probability is an exercise to be treated with great concentration and logic. Indeed, they involve your intelligence and your skills. They are also used in everyday life. A series of corrected ninth grade math exercises on probability will help you practice well. In addition,these exercises involve the following concepts:

• definition of a random experiment;
• definition of an outcome and an event;
• probability tree;
• calculation of probabilities.

## Series of exercises on probabilities

### Exercise 1:

The lottery wheel below is balanced and divided into eight identical sectors.

The wheel is spun and the number spotted is observed. Explain why the event E: “The number found is divisible by 4” and its event
opposite have the same probability.

### Exercise 2:

An opaque bag contains eight tokens numbered from 1 to 8.

A chip is drawn at random and its number is noted. 1. in each case, indicate the outcomes that achieve
the event:

a. Get a multiple of 2″;

b. Get a number greater than or equal to 4″;
c. Get an even number greater than or equal to 4″.

Give the decimal form of each probability.
a. P( ) b. P( ) c.P( )

### Exercise 3 probabilities :

A card is randomly drawn from a deck of 32 cards.

1.a. How many outcomes does the experiment have?
b. What is the probability of each outcome? 2.a. Indicate the outcomes that realize each of the events:

• E: “The suit of the drawn card is red (hearts or diamonds)”;
• F: “The card drawn is an ace”.

b. Give the probability of each of these events.

3.are there outcomes that achieve both events E and F at the same time?
What are they?

### Exercise 4:

The balanced wheel below is divided into ten identical sectors numbered from 1 to 10. Lea spins the wheel and observes the number spotted.
She is interested in the following events:

• E: “The number marked is even”;
• F: “The number identified is a multiple of 3”;
• G:” The number identified is a multiple of 5 “.

1. Make a list of the outcomes that realize each of the events E, F and G.

In each case, say whether the events are incompatible or not. Justify the answer.
a. E and F b. E and G c. F and G

Give the probability of each of the events E, F and G.

### Exercise 5:

Mathis throws a balanced 1€ coin, notes the result:
Heads (H) or Tails (T), then randomly draw a ball from the bag and observe its color: red (R), green (G),
blue (B), black (N) or yellow (J).

1. a. Copy and complete the tree below.  b. How many outcomes does the experiment have?

2.give the probability of each of the events :

• Get the color red”;
• Do not get the yellow color”.
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