# Kayla remembers to set her alarm clock 62% of the time. When she does remember to set her alarm clock, the probability that she will be late for school is 0.20. When she does not remember to set...

Kayla remembers to set her alarm clock 62% of the time. When she does remember to set her alarm clock, the probability that she will be late for school is 0.20. When she does not remember to set it, the probability that she will be late for school is 0.70. Kayla was late today. What is the probability that she remembered to set her alarm clock?

justaguide | Certified Educator

The probability that Kayla remembers to set her alarm clock is 0.62.  When the alarm clock is set, the probability that she will be late for school is 0.20. If the alarm clock is not set there is 0.70 probability of her being late.

The probability that she sets the alarm P(A) = 0.62, the probability that she is late if the alarm is set `P(L|A) = 0.2`

The probability that Kayla is late for school irrespective of whether the alarm is set or not is `P(L) = 0.62*0.2 + (1 - 0.62)*0.7 = 0.39`

The probability that Kayla set the alarm when it is known that she reached late is: `P(A|L) = (P(L|A)*P(A))/(P(L))`

`P(L|A) = 0.2` , `P(L) = 0.39` and `P(A) = 0.62`

Substituting these values gives: `P(A|L) = (0.2*0.62)/0.39`

= `62/195`

If Kyla is late to school, the probability that she had set the alarm the previous night is `62/195`