Explanation needed!!

Question

You roll a fair four-sided die. If the result is 1 or 2, you roll once
more but otherwise, you stop. What is the probability that the sum total of your
rolls is at least 4?

1. 9/8
2. 9/16
3. 3/5
4. 1/16

Comments

is the answer 3?

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Answer is 9/16. btw, i would like to know your approach

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1/4 *2/4 ----for chossing 1 and then 3 or 4 on second trial

1/4*3/4-----for choosing 2 and then 2 or 3 or 4 on second trial

1/4--------for choosing 4 in second trial

hence 1/4 *2/4   + 1/4*3/4    + 1/4

= 9/16

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in 3rd line why not 1/4*1/4?

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In 3rd line, if 4 comes then the target of a sum total of rolls = 4 is achieved right there.

So 1/4 is the probability of getting 4.

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The 3^rd line, refers to a scenario of getting 4 on the 1^st dice. In which case, you are not allowed to roll the dice, for 2^nd time.

So, Probability of getting sum of rolls as atleast 4  => Probability of getting 4 on 1^st dice.

                                                                         => 1/4   <-- only for the scenario we are referring to.