How do you find the probability of at least one thing happening?

How do you find the probability of at least one thing happening?

To find the probability of at least one of something, calculate the probability of none and then subtract that result from 1. That is, P(at least one) = 1 – P(none).

How do you calculate conditional probability?

Conditional probability is calculated by multiplying the probability of the preceding event by the probability of the succeeding or conditional event. Conditional probability looks at the probability of one event happening based on the probability of a preceding event happening.

How do you know if probability is dependent or independent?

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

How do you find the probability of one or more events happening?

Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

What is the probability that only one of the two events occur?

So, the probability that event 1 occurs and event 2 does not is p1⋅(1−p2). Similarly, the probability of event 2 happening and event 1 not happening is p2⋅(1−p1). Thus, the sum of the two probabilities, which is the probability of exactly one of the events happening, is p1⋅(1−p2)+p2(1−p1)=p1+p2−2p1p2.

What does it mean when a probability is independent?

In probability, we say two events are independent if knowing one event occurred doesn’t change the probability of the other event. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn’t change the probability of getting “heads.”

How do you find the probability of a dependent?

If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A).

What is the probability of an event?

Probability of events. Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes. What is the probability to get a 6 when you roll a die? A die has 6 sides, 1 side contain the number 6 that give us 1 wanted outcome in 6 possible outcomes.

How do you find the probability of two dependent events?

Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs. $$P(X \\, and \\, Y)=P(X)\\cdot P(Y\\: after\\: x)$$.

What is the probability that 2 chips are bad?

(Example for one of the terms: to find the probability that exactly 2 chips are bad, keep in mind that any 2 of the 4 chips can be bad, and so multiplication by (4 choose 2) = 6 is needed.) Of course, it is much easier to just find 1 – P (no chips are bad) = 1 – (0.98)^4 than to go through all the calculations for 1, 2, 3, and 4 bad chips.

What book should I read to learn more about probability?

Solutions to Exercises Marked with s from the book Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang c Chapman & Hall/CRC Press, 2014 Joseph K. Blitzstein and Jessica Hwang Departments of Statistics, Harvard University and Stanford University Chapter 1: Probability and counting Counting