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- 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.

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Examples

ex 1:

A single card is chosen from a deck of 52 playing cards. What is the probability of choosing an ace or a heart?

ex 2:

A fair six sided die is rolled. What is the probability of rolling a number divisible by 3, or an even number?

ex 3:

Find the probability of getting exactly 6 heads in 10 tosses.

ex 4:

Find the probability of getting more than 8 heads in 10 tosses.

ex 5:

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?

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Find more worked-out examples in our database of solved problems..

TUTORIAL

**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**

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