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Probability confusion

Hey all! I'm really confused on probability and I just don't using the equations.I'm doing past paper questions trying to figure it out but I've became stuck on this questionOn a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is 12, 16 and 13 respectively. The probability of being late when using these methods of travel is 15 , 25and 110 respectively. (a) Draw a tree diagram to represent this information.(3) (b) Find the probability that on a randomly chosen day (i) Bill travels by foot and is late, (ii) Bill is not late.(4) (c) Given that Bill is late, find the probability that he did not travel on foot.(4)I'm stuck on C and i somehow managed to get all the others myself.I've got the equation of p(f'|L)=P(F'nL)/P(L) but I have no idea as to find p(F'nL) and I have no idea how the MS did it!Thanks in advance!
Original post by JakeRStudent
Hey all! I'm really confused on probability and I just don't using the equations.I'm doing past paper questions trying to figure it out but I've became stuck on this questionOn a randomly chosen day the probability that Bill travels to school by car, by bicycle or on foot is 12, 16 and 13 respectively. The probability of being late when using these methods of travel is 15 , 25and 110 respectively. (a) Draw a tree diagram to represent this information.(3) (b) Find the probability that on a randomly chosen day (i) Bill travels by foot and is late, (ii) Bill is not late.(4) (c) Given that Bill is late, find the probability that he did not travel on foot.(4)I'm stuck on C and i somehow managed to get all the others myself.I've got the equation of p(f'|L)=P(F'nL)/P(L) but I have no idea as to find p(F'nL) and I have no idea how the MS did it!Thanks in advance!


What have you done so far? (Including a picture of your tree diagram if possible)
IMG_3449.jpg
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Original post by rayquaza17
What have you done so far? (Including a picture of your tree diagram if possible)

Theres all my working and how I got the answer for the last question. I just dont understand how I got the answer and it feels like a fluke to me
IMG_3451.jpg490.9KB
Original post by JakeRStudent
IMG_3449.jpg
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Theres all my working and how I got the answer for the last question. I just dont understand how I got the answer and it feels like a fluke to me

Have to attached the right picture? The top one doesn't look like statistics. :tongue:
IMG_3450.jpg
Original post by rayquaza17
Have to attached the right picture? The top one doesn't look like statistics. :tongue:

Yeah you were right, my bad :') Theres the correct one!
Original post by JakeRStudent
IMG_3450.jpg
Yeah you were right, my bad :':wink: Theres the correct one!


Hey I'm really sorry I haven't had the chance to reply, I'm actually away from home for a few days and won't get the chance to check this for you for a short while.

Could anyone else have a look?
Original post by rayquaza17

Could anyone else have a look?


OK. @JakeRStudent , you've got the first parts of this question right. As for that last one, hit it with Bayes' formula:

P(F′∣L)=P(L∣F′)P(F′)P(L∣F′)P(F′)+P(L∣F)P(F) \displaystyle P(F'|L) = \frac{P(L | F' )P(F' )}{P(L | F' )P( F' ) +P(L | F)P(F)}

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