Asked by Lacey Johnson on May 01, 2024
Verified
The probability that Pete will catch fish when he goes fishing is .88.Pete is going to fish 3 days next week.Define the random variable x to be the number of days Pete catches fish.The expected number of days Pete will catch fish is
A) 0.56.
B) 0.88.
C) 2.64.
D) 0.3168.
Random Variable
A variable linked to numerical outcomes produced by random effects.
Expected Number
The mean or average outcome of a random variable in a probability distribution.
Catch Fish
The act of capturing fish as a form of aquatic animal harvesting for food, sport, or commercial purposes.
- Carry out the computation and understanding of expected values within different distributions.
- Implement the concepts of binomial probability.
Verified Answer
JB
james BarrionuevoMay 04, 2024
Final Answer :
C
Explanation :
The probability of catching fish on any given day is 0.88. We can use the binomial distribution to calculate the probability of catching fish on exactly 0, 1, 2, or 3 days:
P(X = 0) = 0.12^3 = 0.001728
P(X = 1) = 3 * 0.88 * 0.12^2 = 0.049152
P(X = 2) = 3 * 0.88^2 * 0.12 = 0.405504
P(X = 3) = 0.88^3 = 0.681472
To find the expected value of X, we multiply each possible value of X by its probability and add them up:
E(X) = 0(0.001728) + 1(0.049152) + 2(0.405504) + 3(0.681472)
E(X) = 1.32
Therefore, the expected number of days that Pete will catch fish is 1.32.
P(X = 0) = 0.12^3 = 0.001728
P(X = 1) = 3 * 0.88 * 0.12^2 = 0.049152
P(X = 2) = 3 * 0.88^2 * 0.12 = 0.405504
P(X = 3) = 0.88^3 = 0.681472
To find the expected value of X, we multiply each possible value of X by its probability and add them up:
E(X) = 0(0.001728) + 1(0.049152) + 2(0.405504) + 3(0.681472)
E(X) = 1.32
Therefore, the expected number of days that Pete will catch fish is 1.32.
Learning Objectives
- Carry out the computation and understanding of expected values within different distributions.
- Implement the concepts of binomial probability.