Question

question 26 of 28
roxanne likes to fish. she estimates that 30% of the fish
she catches are trout, 20% are bass, and 10% are perch.
she designs a simulation.
let 0, 1, and 2 represent trout.
let 3 and 4 represent bass.
let 5 represent perch.
let 6, 7, 8, and 9 represent other fish.
the table shows the simulation results.
what is the estimated probability that at least one of the
next four fish roxanne catches will be a trout?
a. 60%
b. 70%
c. 35%
d. 65%

Explanation:

Step1: Count total simulations

There are \(20\) simulations (since there are \(20\) four - digit numbers in the table).

Step2: Count simulations with no trout

Look for four - digit numbers with no \(0\), no \(1\), and no \(2\).
Numbers with no trout: \(7888\), \(4526\), \(6994\), \(7282\), \(8323\), \(3579\), \(6839\), \(7683\) (count these numbers. There are \(8\) such numbers).

Step3: Calculate probability of no trout

The probability of no trout \(P(\text{no trout})=\frac{\text{Number of no - trout simulations}}{\text{Total simulations}}=\frac{8}{20}=0.4\)

Step4: Calculate probability of at least one trout

Using the formula \(P(\text{at least one trout}) = 1 - P(\text{no trout})\)
\(P(\text{at least one trout})=1 - 0.4=0.6\)

Answer:

A. 60%