Edexcel A-Level Mathematics AS S1.3.3 Independence of Two Events QuestionsPractise testing event independence by comparing intersections with products of probabilities, solving unknowns from independence conditions, and explaining non-independence.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
Edexcel A-Level Mathematics AS S1.3.3 Independence of Two Events Questions 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)Mark as masteredShow AnswerP(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)P(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)34=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)P(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