Yesterday’s Problem, Monty Hall Paradox
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice and why? Give a proper mathematical explanation.
Now here is the solution given by my elder brother
Probability of winning when we don’t switch = (1/2) * (2/3) = 1/3 (probability that car is behind gate 1 and gate 3 has a goat)
Probability of winning when we switch = 1-(1/2)*(2/3) = 2/3.
But here is another solution if you did not understood the above solution. This is from good old Wikipedia.