A cereal company is putting 1 of 4 prizes in each box of cereal. The prizes are evenly distributed so the

probability of winning any given prize is always 1/4.

Lily wonders how many boxes she should expect to buy to get all 4 prizes. She carried out 20 trials of a

simulation and her results are shown below. Each dot represents how many boxes it took to get all 4 prizes in

that trial.

4

5

6

7

8

9

10 11 12 13 14 15

# of boxes purchased

Use her results to estimate the probability that it takes fewer than 7 boxes to get all 4 prizes.

Give your answer as either a fraction or a decimal.

P(fewer than 7 boxes) -

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-04-24T08:44:47+02:00

Answer:

[tex]P(x < 7) = 0.383[/tex]

Step-by-step explanation:

Given

See attachment for plot

Required

Determine the probability that few than 7 boxes will be needed.

This is represented as:

[tex]P(x < 7)[/tex]

And the solution is:

[tex]P(x < 7) = P(x = 4) + P(x = 5) + P(x = 6)[/tex]

Each probability is calculated by dividing the number of dots by the total dots.

So, we have:

[tex]P(x < 7) = \frac{n(x = 4) + n(x = 5) + n(x = 6)}{Total}[/tex]

From the attached, the formula becomes:

[tex]P(x < 7) = \frac{4 + 6 + 3}{4+6+3+4+4+6+3+2+1+2+0+1}[/tex]

[tex]P(x < 7) = \frac{13}{36}[/tex]

[tex]P(x < 7) = 0.361[/tex]