Pearson Edexcel IAL Mathematics S1.3.3 Independence of two eventsPractise testing whether two events are independent by comparing probabilities, intersections and conditional probabilities.SyllabusFirst assessment 2019CourseMathematics YMA01LevelAS
Exam pointsdetermine independence by comparing P(A ∩ B) with P(A)P(B)use independence conditions to solve for an unknown probability in a table or diagramexplain why two events are not independent using a clear probability comparison
S1.3.3 - Independence of two events question 1[Maximum number: 4]The events H and W are such thatP(H)=38P(H∪W)=34\mathrm{P}(H)=\frac{3}{8} \quad \mathrm{P}(H \cup W)=\frac{3}{4}P(H)=83P(H∪W)=43Given that H and W are independent,show that P(W)=35\mathrm{P}(W)=\frac{3}{5}P(W)=53The event N is such thatP(N)=115P(H∩N)=P(N)\mathrm{P}(N)=\frac{1}{15} \quad \mathrm{P}(H \cap N)=\mathrm{P}(N)P(N)=151P(H∩N)=P(N)Show AnswerMark as masteredP(H∪W)=P(H)+P(W)−P(H∩W)\mathrm{P}(H \cup W)=\mathrm{P}(H)+\mathrm{P}(W)-\mathrm{P}(H \cap W)P(H∪W)=P(H)+P(W)−P(H∩W)P(H′∩W)=P(H∪W)−P(H)\mathrm{P}\left(H^{\prime} \cap W\right)=\mathrm{P}(H \cup W)-\mathrm{P}(H)P(H′∩W)=P(H∪W)−P(H)M1P(H∩W)=38×P(W)\mathrm{P}(H \cap W)=\frac{3}{8} \times \mathrm{P}(W)P(H∩W)=83×P(W)}P(H′∩W)=P(H′)×P(W)\mathrm{P}\left(H^{\prime} \cap W\right)=\mathrm{P}\left(H^{\prime}\right) \times \mathrm{P}(W)P(H′∩W)=P(H′)×P(W)M134=38+P(W)−38P(W)\frac{3}{4}=\frac{3}{8}+\mathrm{P}(W)-\frac{3}{8} \mathrm{P}(W)43=83+P(W)−83P(W)}38=58P(W)\frac{3}{8}=\frac{5}{8} \mathrm{P}(W)83=85P(W)A1P(W)=35∗\mathrm{P}(W)=\frac{3}{5} *P(W)=53∗}P(W)=35∗\mathrm{P}(W)=\frac{3}{5} *P(W)=53∗A1cso*(4)Add to Test