The probability of passing geography in the examination is 7/10 and the probability of passing agriculture after one has passed geography is 5/7. The probability of passing agriculture after one failed geography is 1/6. Calculate the probability of a student passing agriculture.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Either-or probabilities are found by adding the individual probabilities.
(.7*5/7) + (.3*1/6) = ?
To calculate the probability of passing agriculture, we need to consider two scenarios: passing geography and failing geography.
1. Probability of passing agriculture given passing geography:
The probability of passing geography is given as 7/10. Therefore, the probability of being in this scenario is 7/10.
The probability of passing agriculture after passing geography is given as 5/7.
To calculate the probability of passing agriculture in this scenario, we multiply the probabilities: (7/10) * (5/7) = 35/70 = 1/2.
2. Probability of passing agriculture given failing geography:
The probability of failing geography is the complement of passing geography, which is 1 - 7/10 = 3/10.
The probability of passing agriculture after failing geography is given as 1/6.
To calculate the probability of passing agriculture in this scenario, we multiply the probabilities: (3/10) * (1/6) = 3/60 = 1/20.
Now, we need to consider both scenarios and calculate the overall probability of passing agriculture:
Overall probability of passing agriculture = Probability of passing agriculture given passing geography + Probability of passing agriculture given failing geography
= (1/2) + (1/20)
= (10/20) + (1/20)
= 11/20
Therefore, the probability of a student passing agriculture is 11/20.