1. mrs. armstead wakes up late on average 4 days in every 5. if mrs.\narmstead wakes up late, the…
1. mrs. armstead wakes up late on average 4 days in every 5. if mrs.\narmstead wakes up late, the probability shes late to work is\n7/10. if mrs. armstead does not wake up late, the probability\nshes late for work is 1/10. what percent of the days does mrs.\narmstead get to work on time? (hint: draw a tree diagram to\nmodel this scenario.)
Answer
Explanation:
Step1: Calculate the probability of waking up late and being on - time
The probability of waking up late (P(L)=\frac{4}{5}), and the probability of being on - time when waking up late (P(O|L)=\frac{9}{10}) (since the probability of being late when waking up late is (\frac{1}{10}), so (1-\frac{1}{10}=\frac{9}{10})). The joint probability (P(L\cap O)=P(L)\times P(O|L)=\frac{4}{5}\times\frac{9}{10}=\frac{36}{50})
Step2: Calculate the probability of waking up not late and being on - time
The probability of waking up not late (P(\overline{L}) = 1-\frac{4}{5}=\frac{1}{5}), and the probability of being on - time when waking up not late (P(O|\overline{L}) = 1) (because if she doesn't wake up late, she is on - time). The joint probability (P(\overline{L}\cap O)=P(\overline{L})\times P(O|\overline{L})=\frac{1}{5}\times1=\frac{10}{50})
Step3: Calculate the total probability of being on - time
Using the law of total probability (P(O)=P(L\cap O)+P(\overline{L}\cap O)). Substitute the values from step 1 and step 2: (P(O)=\frac{36}{50}+\frac{10}{50}=\frac{46}{50})
Step4: Convert the probability to a percentage
To convert (\frac{46}{50}) to a percentage, we use the formula (P(%)=\frac{46}{50}\times100%). (\frac{46}{50}\times100%=(46\times2)% = 92%)
Answer:
(92%)