If the probability that a baby born in a certain hospital will speak in the next day is 1/4, what is the probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow?
+2666 Instead of finding the probability that two or more babies will speak tomorrow, we will find the probability that 0 or 1 babies speak tomorrow and subtract that from 1.
The probability that none of the babies speak tomorrow is \(({3 \over 4})^5 = {243 \over 1024}\)
The probability that exactly 1 baby speaks tomorrow is \({1 \over 4} \times ({3 \over 4})^4 \times {5 \choose 1} = {405 \over 1024}\) (1 baby has to speak, the others must not, and there are 5 ways to choose the baby that does speak)
So, the probability that at least 2 babies speak tomorrow is \(1 - {243 \over 1024} - {405 \over 1024} = {376 \over 1024} = \color{brown}\boxed{47 \over 128}\)
+2666 Melody also answered this here: https://web2.0calc.com/questions/binomial-probability_6
