Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws another tile. What is the sample space of the event representing the letters picked in the two draws? {T-I, T-M, T-E, I-M, I-E, M-E} {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E} {T-I, T-T, T-E, I-T, I-I, I-E, E-T, E-M, E-E, M-T, M-M, M-E} {T-I, T-M, T-E, T-T, I-T, I-M, I-E, I-I, E-T, E-M, E-I, E-E, M-T, M-T, M-E, M-M}

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nestorisaiaguil nestorisaiaguil

15-08-2017
Mathematics

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Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws another tile. What is the sample space of the event representing the letters picked in the two draws? {T-I, T-M, T-E, I-M, I-E, M-E} {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E} {T-I, T-T, T-E, I-T, I-I, I-E, E-T, E-M, E-E, M-T, M-M, M-E} {T-I, T-M, T-E, T-T, I-T, I-M, I-E, I-I, E-T, E-M, E-I, E-E, M-T, M-T, M-E, M-M}

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virtuematane virtuematane · Answer 1 · 2019-05-22T11:01:51+02:00

Answer:

The sample space of events that represent the picking out of letters at two draw without replacing is:

{T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}

Step-by-step explanation:

Since, there are four choice of drawing a first tile:

T I M E

and now:

If first tile is drawn as T then the outcome corresponding to T on second draw are:

T-I T-M T-E

(T-T is not possible since there is no replacement of first tile )

Similarly if I is drawn on first draw then the outcome corresponding to I in second draw is:

I-T I-M I-E

(I-I is not possible since there is no replacement of first tile )

If M is drawn on first draw then the outcome corresponding to M in second draw is:

M-T M-I M-E

(M-M is not possible since there is no replacement of first tile )

Now if E is drawn on first draw then the outcome corresponding to E in second draw is:

E-T E-I E-M

(E-E is not possible since there is no replacement of first tile )

Hence, total outcomes are:

{T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}

MrRoyal MrRoyal · Answer 2 · 2022-02-07T14:32:45+01:00

The sample space of picking two letters without replacement is: {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}

The letters are given as: T I M E

Given that the selection is without replacement, we have the following number of possibility:

[tex]n = 4^2[/tex]

Where:

4 is the number of letters

2 is the number of selection

So, we have:

[tex]n = 16[/tex]

The selections are then represented as:

TI, TM, TE

IT, IM, IE

MT, MI, ME

ET, EI, ET

Hence, the sample space without replacement is: {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}