Home / Khoa học / conditional probability Conditional Probability 25/09/2021 P(A/B) is known as conditional probability & it means the probability of sự kiện A that depends on another event B. It is also known as "the probability of A given B". P(A/B) Formula is used lớn find this conditional probability quickly.Bạn đang xem: Conditional probabilityWhat IsP(A/B) Formula?The conditional probability P(A/B) arises only in the case of dependent events. It givesthe conditional probability of Agiven that Bhas occurred.P(A/B) Formula:P(A/B) =P(A∩B) / P(B)Similarly, the P(B/A) formula is: P(B/A) =P(A∩B) / P(A)Here,P(A) = Probability of sự kiện A happening.P(B) = Probability of event Bhappening.P(A∩B) =Probability of happening of both A và B.From these two formulas, we can derive the sản phẩm formulas of probability.P(A∩B) = P(A/B) ×P(B)P(A∩B) = P(B/A) ×P(A)Note:If A và B are independent events, thenP(A/B) = P(A)or P(B/A) = P(B)Have sầu questions on basic mathematical concepts?Become a problem-solving champ using súc tích, not rules. Learn the why behind math with our certified expertsBook a Free Trial ClassExamples UsingP(A/B) FormulaExample 1:When a fair die is rolled, what is the probability of A given B where A is the sự kiện of getting an odd number and B is the event of getting a number less than or equal to 3?Solution:To find: P(A/B) using the given information.When a die is rolled, the sample space = 1, 2, 3, 4, 5, 6.A is the event of getting an odd number. So A = 1, 3, 5.B is the event of getting a number less than or equal to 3. So B = 1, 2, 3.Then A∩B = 1, 3.Xem thêm: Tin Thể Thao Tin Thể Thao Bóng Đá Hôm Nay, Tin Thể Thao Nhanh 24/7 MớiUsing theP(A/B) formula:P(A/B) =P(A∩B) / P(B)(P(A/B) = dfrac2/63/6 = dfrac 2 3)Answer: P(A/B) = 2 / 3.Example 2:Two cards are drawn from a deông chồng of 52 cards where the first thẻ is NOT replaced before drawing the second thẻ. What is the probability that both cards are kings?Solution:To find:The probability that both cards are kings.P(card 1 is a king) = 4 / 52 (as there are 4 kings out of 52 cards).P(card 2 is a king/thẻ 1 is a king) = 3 / 51 (as the first king is not replaced, there is a totalof 3 kings out of 51 left out cards).Bythe formula of conditional probability,P(thẻ 1is a king ∩thẻ 2is a king) =P(thẻ 2 is a king/thẻ 1 is a king) ×P(card 1 is a king)P(thẻ 1is a king ∩card 2is a king) = 3 / 51 ×4 / 52 = 1 / 221Answer: The required probability= 1 / 221.FAQs onP(A/B) FormulaWhat IsP(A/B) Formula?P(A/B) Formula is the formula used to lớn calculate the conditional probability such that we have to lớn find the probability of event 'A' occurring when event 'B' has occurred.P(A/B) Formula is given as,P(A/B) =P(A∩B) / P(B), where,P(A) is probability of event A happening, P(B) isthe probability of event Bhappening andP(A∩B) is the probability of happening of both A và B.How to FindP(A∩B) UsingP(A/B) Formula?P(A∩B) can be calculated using theP(A/B) Formula as,P(A∩B) = P(A/B) ×P(B), where, P(B) isthe probability of event Bhappening & P(A∩B) is the probability of happening of both A & B.What Is ∩ Symbol inP(A∩B) Formula?P(A/B) Formula is given as,P(A/B) =P(A∩B) / P(B), here∩ symbol represents the intersection of sự kiện 'A' and event 'B'.P(A) is probability of sự kiện A happening, P(B) isthe probability of sự kiện Bhappening andP(A∩B) is the probability of happening of both A and B.