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- Probability Calculator
Probability calculator
This calculator computes the probability of a selected event based on the probability of other events. The calculator uses the addition rule, multiplication rule, and Bayes theorem to find conditional probabilities.The calculator generates a solution with a detailed explanation.
A single card is chosen from a deck of 52 playing cards. What is the probability of choosing an ace or a heart?
A fair six sided die is rolled. What is the probability of rolling a number divisible by 3, or an even number?
Find the probability of getting exactly 6 heads in 10 tosses.
Find the probability of getting more than 8 heads in 10 tosses.
If a player scores 3 out of 5 free throws, what is the probability that he will score more than 9 out of 12 attempts?
Basic Rules for Finding Probabilities
The addition rule is used to find the probability that event A or event B occurs. To apply this rule, we need to add probabilities for events A and B and then subtract the probability of intersection. So for the union of two events, we have the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
Example 1: Consider families with two children. Let A be the event that the first child is a girl, and B be the event that the second child is a girl. In this case, P(A and B) is the probability that both children are girls, and P(A or B) is the probability that at least one child is a girl. If we know that P(A) = 1/2, P(B) = 1/2, and P(A and B) = 1/4, then:
P(A or B) = P(A) + P(B) - P(A and B) = 1/2 + 1/2-1/4 = 3/4
The multiplication rule is used to find the probability that events A and B both occur. For independent events, multiplication rule is P(A and B) = P(A) × P(B) and for dependant events, the formula is: P(A and B) = P(A) × P(B|A).
Example 2: Suppose we flip the coin three times. What is the probability of getting all three heads?
Let A be the event that we get a head on a single coin toss. The P(A) is 1/2. The P(AAA) is:
P(AAA) = P(A) × P(A) × P(A) = 1/2 × 1/2 × 1/2 = 1/8