A1 A1 cao 3 14 a P(late) = 0.08 M1 2 M1 for correct multiplication for three different events M P(not late) = 0.92 oe P(early) = 0.02 P(not early) = 0.98 P(raining) = 0.3 P(not raining) = 0.7 P(on time) = 1 P(late) P(early) – – = 1 0.02 –0.08 – = 0.9 P(on time, not raining) = 0.9 × 0.7 = 0.63 P(on time, not raining) = 0.63 b P(raining, raining, raining) = 0.33 M1 M1 for correct multiplication for three same events oe P(raining, raining, raining) = 0.027 =0.027 c P(not late five days in a row) = 0.925 P(not late five days in a row) = 0.659 = 0.6591 M1 M1 for correct multiplication for five same complement events oe 3 15 Let the number of students in the class The number of students who took the P1 2 P1 for either solving the linear equation or calculating, H exam is 40. using the percentages from the Venn diagram be x. Number who solve problem 1 = 0.5x Number who solve problem 2 = 0.8x C1 C1 for explanation as to why 12 is subtracted (or we have 30% too much) So is the two added together less 12 as x this has been counted twice = 0.8x + 0.5x 12 x – 1.3x 12 x= – 12 = 0.3x 40 x=
A1 A1 cao 3 14 a b c P(late) = 0.08 P(not late) = 0.92 P(early) = 0.02 P(not early) = 0.98 P(raining) = 0.3 P(not raining) = 0.7 P(on time) = 1 – P(late) – P(early) = 1 –0.08 – 0.02 = 0.9 P(on time, not raining) = 0.9 × 0.7 = 0.63 P(raining, raining, raining) = 0.33 =0.027 P(not late five days in a row) = 0.925 = 0.6591 P(on time, not raining) = 0.63 P(raining, raining, raining) = 0.027 P(not late five days in a row) = 0.659 M1 M1 M1 2 M1 for correct multiplication for three different events oe M1 for correct multiplication for three same events oe M1 for correct multiplication for five same complement events oe M 3 15 Let the number of students in the class be x. Number who solve problem 1 = 0.5x Number who solve problem 2 = 0.8x So x is the two added together less 12 as this has been counted twice x = 0.8x + 0.5x – 12 x= 1.3x – 12 12 = 0.3x x= 40 The number of students who took the exam is 40. P1 C1 2 P1 for either solving the linear equation or calculating, using the percentages from the Venn diagram C1 for explanation as to why 12 is subtracted (or we have 30% too much) H
Higher_Skills_Probability_MarkScheme_Edexcel.docx