Probability of independent and dependent events
key notes :
Two events are independent if the outcome of the first event does not affect the outcome of the second event.
The only factors of a prime number are 1 and itself. The number 1 is neither prime nor composite.
The probability is the number of favorable outcomes out of the number of possible outcomes.
Learn with an example
➡️ You roll a 6-sided die two times.
What is the probability of rolling a number less than 4 and then rolling a prime number?
Write your answer as a percentage.
______ %
The events less than 4 and prime are independent. The first roll does not affect the second roll.
Find P(less than 4). The die has 6 sides, numbered 1, 2, 3, 4, 5 and 6. The numbers less than 4 are 1, 2 and 3. There are 3 numbers less than 4.
P(less than 4) = 3/6
Find P(prime). The prime numbers are 2, 3 and 5.
P(less than 4) x P(prime) = 3/6 x 3/6
= 9/36
Write your answer as a decimal. Then convert your answer to a percentage.
9/36 = 0.25 = 25%
The probability of rolling a number less than 4 and then rolling a prime number is 25%.
➡️ You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
Find P(even). There are 4 cards, numbered 1, 2, 3 and 4. The even numbers are 2 and 4. There are 2 even numbers.
P(even) = 2/4
Now find the probability of picking an even number once you have already picked an even number.
There are 3 cards remaining. One of those cards is an even number.
After you have picked an even number, the probability of picking an even number is 1/3 ,
Find the probability of picking an even number and then picking an even number. Multiply P(even) by P(even).
P(even) x P(even) = 2/4 x 1/3
= 2/12
Write your answer in simplest form.
2/12 = 1/6
The probability of picking an even number and then picking an even number is 1/6 .
➡️ You roll a 6-sided die two times.
What is the probability of rolling a factor of 12 and then rolling a number less than 4?
Simplify your answer and write it as a fraction or whole number.
The events factor of 12 and less than 4 are independent. The first roll does not affect the second roll.
Find P(factor of 12). The die has 6 sides, numbered 1, 2, 3, 4, 5 and 6. The factors of 12 are 1, 2, 3, 4 and 6.
P(factor of 12) = 5/6
Find P(less than 4). The numbers less than 4 are 1, 2 and 3. There are 3 numbers less than 4.
P(less than 4) = 3/6
Find the probability of rolling a factor of 12 and then rolling a number less than 4. Multiply P(factor of 12) by P(less than 4).
P(factor of 12) x P(less than 4) = 5/6 x 3/6
= 15/36
Write your answer in simplest form.
15/36 = 5/12
The probability of rolling a factor of 12 and then rolling a number less than 4 is 5/12 .
let’s practice!
