probability 🦭

Question 1

A jar consists of 21 sweets. 12 are green and 9 are blue. William picked two sweets at random. What is the probability he will pick 1 green sweet and 1 blue sweet? How do I solve this?

Answer 1

Step 1: Determine the total number of sweets
T = 21 (12 green, 9 blue)

Step 2: Calculate total ways to pick 2 sweets from 21
1st try - 21 sweets, 2nd try - 20 sweets
Number of sweets to pick: 2
(21*20)/2

Step 3: Calculate ways to pick 1 green & blue sweet
- 12 green -> 1/12
- 9 blue -> 1/9
Now, multiply them.
12*9 = 108

Step 4: Calculate & simplify
(ways to pick 1 green and blue)/(total ways to pick 2 sweets)
Probability = 108/210
Simplified = 18/35

Question 2

Theoretical probability formula

Answer 2

P(A) = (Number of favourable outcomes) / (Number of possible outcomes)

Question 3

Experimental probability formula

Answer 3

P(A) = (Number of times event A occurs) / (Total number of trials)

Question 4

A student conducts an experiment by rolling a six-sided die 60 times to determine the experimental probability of rolling a 4. How can I solve this question?

Answer 4

Step one: divide the number of trials by 4
60/4 = 15

Step two: Divide the number of times the event occurs by the total number of trials
p(a) = 15/60

Step three: Simplify
1/4 or 0.25 is the answer

Question 5

Conditional probability

Answer 5

P(A|B) = P(A ∩ B) / P(B)