An egg distributer determines that the probability that any individual egg has a

Daniaal Sanchez 2021-09-18 Answered
An egg distributer determines that the probability that any individual egg has a crack is 0.15.
​a) Write the binomial probability formula to determine the probability that exactly x eggs of n eggs are cracked.
​b) Write the binomial probability formula to determine the probability that exactly 2 eggs in a​ one-dozen egg carton are cracked. Do not evaluate.
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Expert Answer

cheekabooy
Answered 2021-09-19 Author has 83 answers
Step 1
Some characteristics of binomial distribution:
Each trial has exactly two possible outcomes.
There are n number of trials, in which p is the probability of success and q(=1p) is the probability of failure.
The trials are independent of each other.
The probability of success in each trial remains constant.
Formula for binomial probability:
The formula for binomial probability is as follows.
P(X=x)=ncxpxq(nx)
where,
p is the probability of success,
q is the probability of failure,
n is the number of questions
Step 2
a) Binomial probability formula to determine the probability that exactly x eggs of n eggs are cracked:
Here, the event of success is “eggs that have cracks”.
The probability of success (an individual egg has a crack) is, p=0.15.
The probability of failure is, q=10.15=0.85.
The binomial probability formula to determine the probability that exactly x eggs of n eggs are cracked is as follows.
P(X=x)=ncx(0.15)x(0.85)(nx)
Step 3
b) Binomial probability formula to determine the probability that exactly 2 eggs in a one-dozen egg carton are cracked:
In general, number of eggs in one-dozen egg carton is, n=12.
The binomial probability formula to determine the probability that exactly 2 eggs in a one-dozen egg carton are cracked is as follows.
P(X=2)=12C2(0.15)2(0.85)(122)
=12C2(0.15)2(0.85)10
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