Bob catches a train to work every day from monday to friday. the probability that the train is late on monday is 0.45. the probability that the train is late on any other day is 0.3. A day is chosen at random. Find the probability it is monday and the train is late
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(Monday) = 1/7
P(late) = .45
To find the probability that it is Monday and the train is late, we can multiply the probability that it is Monday by the probability that the train is late on Monday.
Given:
- Probability that the train is late on Monday is 0.45.
- Probability that the train is late on any other day (Tuesday to Friday) is 0.3.
Let's calculate the probability:
Probability of it being Monday = 1/5 (since there are 5 weekdays and each day is equally likely to be chosen at random)
Probability of the train being late on Monday = 0.45
Probability that it is Monday and the train is late = Probability of it being Monday * Probability of the train being late on Monday
Probability that it is Monday and the train is late = (1/5) * 0.45 = 0.09
Therefore, the probability that it is Monday and the train is late is 0.09 or 9%.