I would like to know why you multiplied 0.5 seven times.
did you arrive to your answer by using this formula:
??
found this question on a website , it gives the answer as 0.27
but it doesn't show how the author arrived at the answer
ive never dealed with replacement before
A bag contains 5 yellow beads and 5 blue beads (all identical apart from the colour).
7 beads are drawn randomly from the bag, each being replaced before the next is drawn.
Calculate the probability that
Exactly 4 of the beads drawn are yellow
7! / 4! 3! = 35 * multiplied by 0.5 seven times= 0.2734
I dont know if the formula used is correct
or i simply got lucky and matched authors answer ?
so the new question would be
A bag contains 6 yellow beads and 4 blue beads (all identical apart from the colour).
7 beads are drawn randomly from the bag, each being replaced before the next is drawn.
Calculate the probability that
Exactly 4 of the beads drawn are yellow
7! / 4! 3! * 0.6 *0.6 *0.6 * 0.6 * 0.4 * 0.4 * 0.4 = 0.2903
Right.
So your answers are correct in both the cases. And the formula you are using is correct indeed!
Note that you are using the same formula I have written in post #2.
Here's an explanation(your original question):
since there are 5 yellow and 5 blue beads,
the probability of obtaining a yellow bead
the probability of obtaining a yellow bead
Total number of balls = 7.
Let X be the number of yellow balls drawn. then,
the probability of 4 yellow balls being drawn is: