Sick days

In Canada, there are typically 261 working days per year. There is a 4.9% chance of an employee taking a sick day.
What is the probability an employee will use 17 OR MORE sick days in a year?

Correct answer:

p =  0.1442

Step-by-step explanation:

q=4.9%=1004.9=0.049 n=261  C0(261)=(0261)=0!(2610)!261!=11=1  p0=(0261) q0 (1q)n0=1 0.0490 (10.049)26102.0189106 C1(261)=(1261)=1!(2611)!261!=1261=261  p1=(1261) q1 (1q)n1=261 0.0491 (10.049)26112.715105 C2(261)=(2261)=2!(2612)!261!=21261260=33930  p2=(2261) q2 (1q)n2=33930 0.0492 (10.049)26120.0002 C3(261)=(3261)=3!(2613)!261!=321261260259=2929290  p3=(3261) q3 (1q)n3=2929290 0.0493 (10.049)26130.0008 C4(261)=(4261)=4!(2614)!261!=4321261260259258=188939205  p4=(4261) q4 (1q)n4=188939205 0.0494 (10.049)26140.0027 C5(261)=(5261)=5!(2615)!261!=54321261260259258257=9711475137  p5=(5261) q5 (1q)n5=9711475137 0.0495 (10.049)26150.0071 C6(261)=(6261)=6!(2616)!261!=654321261260259258257256=414356272512  p6=(6261) q6 (1q)n6=414356272512 0.0496 (10.049)26160.0157 C7(261)=(7261)=7!(2617)!261!=7654321261260259258257256255=15094407070080  p7=(7261) q7 (1q)n7=15094407070080 0.0497 (10.049)26170.0294 C8(261)=(8261)=8!(2618)!261!=87654321261260259258257256255254=479247424475040  p8=(8261) q8 (1q)n8=479247424475040 0.0498 (10.049)26180.0481 C9(261)=(9261)=9!(2619)!261!=987654321261260259258257256255254253=13472177599131680  p9=(9261) q9 (1q)n9=13472177599131680 0.0499 (10.049)26190.0696 C10(261)=(10261)=10!(26110)!261!=339498875498118336  p10=(10261) q10 (1q)n10=339498875498118336 0.04910 (10.049)261100.0904 C11(261)=(11261)=11!(26111)!261!=7746747068184336576  p11=(11261) q11 (1q)n11=7746747068184336576 0.04911 (10.049)261110.1063 C12(261)=(12261)=12!(26112)!261!1.613×1020=161390563920507012000  p12=(12261) q12 (1q)n12=161390563920507012000 0.04912 (10.049)261120.1141 C13(261)=(13261)=13!(26113)!261!3.091×1021=3091250032015865076000  p13=(13261) q13 (1q)n13=3091250032015865076000 0.04913 (10.049)261130.1126 C14(261)=(14261)=14!(26114)!261!5.475×1022=54759286281423895632000  p14=(14261) q14 (1q)n14=54759286281423895632000 0.04914 (10.049)261140.1028 C15(261)=(15261)=15!(26115)!261!9.017×1023=901702914100780148073600  p15=(15261) q15 (1q)n15=901702914100780148073600 0.04915 (10.049)261150.0872 C16(261)=(16261)=16!(26116)!261!1.386×1025=13863682304299494776631600  p16=(16261) q16 (1q)n16=13863682304299494776631600 0.04916 (10.049)261160.0691  s=p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11+p12+p13+p14+p15+p16=2.0189106+2.715105+0.0002+0.0008+0.0027+0.0071+0.0157+0.0294+0.0481+0.0696+0.0904+0.1063+0.1141+0.1126+0.1028+0.0872+0.06910.8558 p=1s=10.8558=0.1442



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