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i just need a double check on my solution for the task below; The probability that roads are slippery during winter is 30% On slippery roads, there is a risk of traffic jams caused by accidents by 70% On clear roads the risk of a traffic jam is just 20% What is the probability that the road was slippery when Mrs Joans was caught up in a traffic jam?

S - event that the road is slippery = 30% NS - event that the road is not slippery = 70% T = Traffic Jam S - Slippery NS - Not Slippery

P(T|S) = 70% P(T|NS) = 20%

P(S|T) = P(T|S)P(S) / P(T|S)P(S) + P(T|NS)P(NS) = (0.7)(0.3)/(0.7)(0.3) + (0.2)(0.7) = 60%

Thanks

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    what do you think is wrong? i cant check the results if it is correct or not so thats why I am double checking it here. according to the answer from Elika below, my calculations are correct. Please let me know how you did it, – 2017-01-30

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Your result is correct. Here, the conditional probability is correctly calculated by an application of Bayes' theorem.

However, I see two "mistakes" in your answer:

1.) You are missing brackets in the denominator of Bayes' Theorem (but the result is correct)

2.) You should be more carefully with your notation when defining the events and writing down their probability. i.e. do not write

"S - event that the road is slippery EVENT = 0.3"

instead separate the event from its probability as the event $S$ and its probability $P(S)$ are two different shoes.

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    Thanks Elika. will take note to correct the mistakes. – 2017-01-30