At a petrol station, 90% of the customers use RON95 fuel, 5% use RON97 fuel and 5% use diesel fuel. Suppose that 75%, 80% and 90% of RON95 users, RO

[TONG]

At a petrol station, 90% of the customers use RON95 fuel, 5% use RON97
fuel and 5% use diesel fuel. Suppose that 75%, 80% and 90% of RON95
users, RON97 users and diesel users fill their tanks, respectively. At this
station, a customer just filled her tank. What is the probability that she used
RON95 fuel?

 

[Deleted member 4993]

At a petrol station, 90% of the customers use RON95 fuel, 5% use RON97 fuel and 5% use diesel fuel. Suppose that 75%, 80% and 90% of RON95 users, RON97 users and diesel users fill their tanks, respectively. At this station, a customer just filled her tank. What is the probability that she used RON95 fuel?

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[HallsofIvy]

Suppose there are 10000 customers. 90% of them, 9000, use RON95, 5%, 500, use RON97, and the other 500 use diesel. Of the 9000 who use RON97, 75%, 6750, fill their tanks, of the 500 who use RON95, 80%, , 400, fill their tanks, and of the 500 who use diesel, 90%, 450, fill their tanks. That is a total of 6750+ 400+ 450= 7600 customers who fill their tanks of which 400 use RON95.