Question

The following discrete probability distribution shows the probability of having the indicated number of cracked eggs, X, in each carton of 12 eggs purchased in a certain grocery chain.

X	0	1	2	3	4
P(X)	60%	17%	11%	10%	2%

Tip

"At least 5" means "5 or more"

"At most 5" means "5 or less"

Find each of the following probabilities:

a. P(X < 3) =

b. P(X > 4) =

c. P(1 < X < 4) =

d. P(X ≠ 0) =

e. Probability that a randomly selected carton will contain at least 3 cracked eggs =

f. Probability that a randomly selected carton will contain at most 2 cracked eggs =

Answer 1

The probabilities here are computed from the given probability distribution as:

a) P(X < 3) = 1 - P(X = 3) - P(X = 4) = 1 - 0.1 - 0.02 = 0.88
Therefore 0.88 is the required probability here.

b) P(X > 4) = 0 as the max value of X can be 4 here. Therefore 0 is the required probability here.

c) P(1 < X < 4) = P(X = 2) + P(X = 3) = 0.11 + 0.1 = 0.21
Therefore 0.21 is the required probability here.

d) P(X not equal to 0) = 1 - P(X = 0) = 1 - 0.6 = 0.4
Therefore 0.4 is the required probability here.

e) P(X >= 3) = P(X = 3) + P(X = 4) = 0.1 = 0.02 = 0.12
Therefore 0.12 is the required probability here.

f) The probability here is computed as:
P(X <= 2) = P(X < 3) = 0.88
Therefore 0.88 is the required probability here.