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Jose is going to use a random number generator 500 times. Each time he uses it, he will get a
1,2,3, or 4.
Complete the following statement with the best prediction.
Jose will get something other than a 2 ...
Choose 1 answer:
(A) Exactly 250 times
(B) Close to 250 times but probably not exactly 250 times
(C) Exactly 375 times
(D) Close to 375 times but probably not exactly 375 times

Jose is going to use a random number generator $500$ times. Each time he uses it, he will get a $1,2,3$ , or $4$ . $\newline$ Complete the following statement with the best prediction. $\newline$ Jose will get something other than a $2$ ... $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $250$ times $\newline$ (B) Close to $250$ times but probably not exactly $250$ times $\newline$ (C) Exactly $375$ times $\newline$ (D) Close to $375$ times but probably not exactly $375$ times

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Find probabilities using combinations and permutations

Full solution

Q. Jose is going to use a random number generator

500

times. Each time he uses it, he will get a

1,2,3

, or

4

.

\newline

Complete the following statement with the best prediction.

\newline

Jose will get something other than a

2

...

\newline

Choose

1

answer:

\newline

(A) Exactly

250

times

\newline

(B) Close to

250

times but probably not exactly

250

times

\newline

(C) Exactly

375

times

\newline

(D) Close to

375

times but probably not exactly

375

times

Understand probability: Understand the probability of getting a number other than $2$ . Since there are four possible outcomes ( $1$ , $2$ , $3$ , or $4$ ) and only one of them is a $2$ , the probability of getting a number other than $2$ is the probability of getting a $1$ , $3$ , or $4$ . There are three favorable outcomes out of four possible outcomes. Probability of not getting a $2$ = Number of favorable outcomes / Total number of outcomes = $1$ $1$ .
Predict number of times: Predict the number of times Jose will get a number other than $2$ . $\newline$ To find the expected number of times Jose will get a number other than $2$ , multiply the total number of trials by the probability of not getting a $2$ . $\newline$ Expected number of times $=$ Total number of trials $*$ Probability of not getting a $2$ $= 500 \times (3/4)$ .
Calculate expected number: Calculate the expected number of times Jose will get a number other than $2$ . $\newline$ Expected number of times = $500 \times \left(\frac{3}{4}\right) = 500 \times 0.75 = 375$ .
Choose best prediction: Choose the best prediction based on the calculation. $\newline$ The calculation shows that the expected number of times Jose will get a number other than $2$ is $375$ . However, since the outcome of each trial is random, it is unlikely to be exactly $375$ times. The best prediction is that it will be close to $375$ times but probably not exactly $375$ times.

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