The question goes as follows: A jar contains 10 balls, 8 are red and 2 are green

Question

The question goes as follows: A jar contains 10 balls, 8 are red and 2 are green. The ballsare drawn out of the jar one at a time without replacement. What isthe probability that the second green ball will be drawn on theseventh draw? I need help on how to approach this question, Thank you! The question goes as follows: A jar contains 10 balls, 8 are red and 2 are green. The ballsare drawn out of the jar one at a time without replacement. What isthe probability that the second green ball will be drawn on theseventh draw? I need help on how to approach this question, Thank you!

Explanation / Answer

The approach is as follows.
We want the probability of second green ball will be theseventh drawn ball.
let us think of a sequence with 8 Rs and 2 Gs.
eg: RRRRG RRRRG or GG RRRRRRRR each ofthese sequences correspond to one possible draw.
Now we want all such sequences where second G is in 7th placeeg: RRRRRGGRRR or GRRRRRGRRR etc....
so our P(second G will be the seventh drawsn ball ) = # ofsuch sequences where 7th place will be second G/ Total number ofsequences possible.
Total number of sequences possible = number of ways you pick 2places for the two Gs ... (remember you need not do any thingelse.. because one you pick 2 places for two Gs the others will beautomatically be given to Rs)
= 10C2 = 45
# of such sequences where second G is in 7th places = # ofways of picking one place for first G in the first 6places
= 6C1 = 6
therefore P(second G will be the seventh drawsn ball ) =6/45 = 13.33 %
Hope it helps you. Feel free to ask for anyclarifications.

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