SOLUTION: there are 3 red and 4white balls in box four balls are selected with replacement from the box. find probability by bernoill trial of event 1 2red ball and 2 white 2 all 4 balls whi

Question 1087210: there are 3 red and 4white balls in box four balls are selected with replacement from the box. find probability by bernoill trial of event 1 2red ball and 2 white 2 all 4 balls white.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
there are 3 red and 4white balls in box four balls are selected with replacement from the box. find probability by bernoill trial of event 1 2red ball and 2 white 2 all 4 balls white.

Solution:
The situation satisfies conditions for a binomial distribution, verified as follows:
1. Bernoulli trials, i.e. exactly two possible outcomes (red=success, white = failure)
2. Number of trials is known before and constant throughout the experiment (4), i.e. independent of outcomes.
3. All trials are independent of each other (satisfied from context)
4. Probability of success is known, and remain constant throughout trials (P(red)=3/7 balls are replaced)

Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given by
P(x)=C(N,x)(p^x)(1-p)^(N-x)
and,
C(N,x) is number of combinations of selecting x objects out of N.

p=P(red)=3/7
n=4

(a) P(2 red and 2 white) => x=2
=C(4,2)(3/7)^2(4/7)^2
=864/2401 [note: fractions give exact probability values]
=0.35985 approximately

(b) P(4 whites) => x=0
=C(4,0)(3/7)^0(4/7)^4
=256/2401
=0.10662 approximately
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