Question

Four students join the entrance exam of a university. The probabilities that they will be accepted are 3/20, 2/17, 1/5 and 1/3 respectively. What is the probability that at least one is accepted??

Answer 1

at least 1 means
1 accepted or 2 accepted or 3 accepted or 4 accepted

Answer 2

one accepted means the first or the second or the third or the fourth
3/20+2/17+ 1/5+1/3=817/1020

two accepted means that 1 and 2 or 1 and 3 or 1 and 4 or 2 and 3 or 2 and 4 or 3 and 4
3/20*2/17+ 3/20* 1/5+ 3/20*1/3+2/17*1/5+2/17*1/3+ 1/5*1/3=193/850

three accepted means 1 and 2 and 3 or 1 and 2 and 3 or 1 and 3 and 4 or 2 and 3 and 4
3/20*2/17* 1/5+ 3/20* 1/5*1/3+ 2/17* 1/5*1/3=109/5100

four accepted means 1 and 2 and 3 and 4
3/20*2/17*1/5*1/3=1/850

now as i said at least 1 means
1 accepted or 2 accepted or 3 accepted or 4 accepted

817/1020+193/850+109/5100+1/850=893/850

xD which seems wrong

Answer 3

@ganeshie8

Answer 4

i think we can tackle this in a different way
probability of none of them being accepted =
(17/20) * (15/17)*(4/5)*(2/3) = 2/5

so required probabilty 9 at least one) = 1 - 2/5 = 3/5

Answer 5

* probability of at least 1