What is the probability that the sum of two dice rolls will yield a 5,

Question

What is the probability that the sum of two dice rolls will yield a 5, and then when both are thrown again, their sum will yield a 9?

A. 1/81
B. 2/81
C. 1/27
D. 4/81
E. 5/81

nick1816 · Answer

Number of ways to get 5=4  
Probability of getting 5 = 4/36=1/9

Number of ways to get 9=4  
Probability of getting 9 = 4/36=1/9

probability that the sum of two dice rolls will yield a 5, and then when both are thrown again= {1/9}*{1/9}=1/81 (as both are independent events)

Kinshook · Answer

14,41,23,32 will yield sum of 5 = 4 cases
63,36,54,45 will yield sum of 9 = 4 cases
Probability (sum=5) = 4/36 = 1/9
Probability (sum=9) = 4/36 = 1/9
Probability (sum=5 & then sum = 9) = 1/9 * 1/9 = 1/81 (Independent events)

IMO A

MayankSingh · Answer

Total outcome =36
5 = (1,4) (2,3) (4,1) (3,2)
9 = (3,6) (4,5) (6,3) (5,4)

Prob= P (5)*P(9)= 4/36 * 4/36= 1/81

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Lampard42 · Answer

Total possibilities for 2 dies = 6 (1st one)* 6(2nd one) =36
Possibility for sum of 5 = (2,3),(3,2),(1,4),(4,1) = 4
Possibility for sum of 9 = (6,3),(3,6),(5,4),(4,5) = 4
Prob. of 5 then 9 = 4/36*4/36=1/81 IMO A

Archit3110 · Answer

sum = 5 ; 1,4; 2,3; 3,2 ; 4,1
total 36 ; 4/36
and sum ; 9 ; 3,6 ; 4,5; 5,4 ; 6,3 ; 4
total 4/36
1/9* 1/9 ; 1/81
IMO A

CareerGeek · Answer

When 2 dice are rolled, total outcomes = 36
Favourable for sum 5 = (1,4), (2,3), (3,2), (4,1) = 4
Favourable for sum 9 = (3,6), (4,5), (5,4), (6,3) = 4
Probability of sum 5 & sum 9
= 4/36*4/36
= 1/9*1/9
= 1/81

IMO Option A

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BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=qGFMqcZ0JHo

We need to find What is the probability that the sum of two dice rolls will yield a 5, and then when both are thrown again, their sum will yield a 9?

As we are rolling two dice => Number of cases =  6^2  = 36

Now for the sum to be 5 we need to find out what comes in both the dice roll. Following outcomes will yield 5 as the sum
(1,4), (2,3), (3,2), (4,1) = 4 outcomes

=> Probability that the sum of two dice will yield a 5 =  \frac{4}{36}  =  \frac{1}{9}

Now, when both are thrown again and we need to get the sum as 9

=> Following cases are possible
(3,6), (4,5), (5,4), (6,3) = 4 cases

=> Probability that the sum of two dice will yield a 9 =  \frac{4}{36}  =  \frac{1}{9}

Probability that these events will happen one after the other = Product of their probabilities =  \frac{1}{9}  *  \frac{1}{9}  =  \frac{1}{81}

So,  Answer will be A 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

What is the probability that the sum of two dice rolls will yield a 5,

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What is the probability that the sum of two dice rolls will yield a 5,

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