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Effectus [21]
3 years ago
13

Shiela either walks or cycles to school the probability that she walks is 0.65 if she walks the probability that she is late is

0.4 if she cycles the probability that she is late is 0.1 What is the probability that she will not be late for school
Mathematics
1 answer:
Serjik [45]3 years ago
3 0

Answer:

0.705

Step-by-step explanation:

Data:

walks=0.65 and is late=0.4;is not late=0.6

cycles=0.35 and is late=0.1;is not late=0.9

The probability of sheila walking and not being late:  

0.65 x 0.6=0.39  

AND probability of being not late and cycling:

0.35 x 0.9=0.315

therefore,the probability of sheila walking or cycling and still not being late:

0.39+0.315=0.705

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 To solve the following problems, we use the binomial probability equation:

P (r) = [n!/(n-r)! r!] p^r q^(n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

 

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

 

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

 

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 – 0.43

P (r ≤ 5) = 0.57

 

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