edited by
2,078 views
2 votes
2 votes

Probability of getting a total of 7 atleast once in three toss of a fair die is

  • 125/216
  • 91/216
  • 117/216
  • 9/216
edited by

4 Answers

2 votes
2 votes
let Y be the event for getting total of 7

P(Y)=1/6

Atleast once means 1-(none)

using binomial =nCx * p^x * q^(n-x)

take x=0 for none and n=3..since tossing 3 times

                        =3c0 * (1/6)^0 * (5/6)^(3)

                        =(5/6)^3

so ans is 1-(5/6)^3 that is (91/216)
1 votes
1 votes

The easiest way,

Probabilty of getting 7 is 1/6 [(1,6),(2,5),(3,4)]*2=6/36=1/6

p(Sum=7)=1/6 and thus, p(Sum is not 7)=5/6

Now, imagine 3 places,

_ _ _

Case-1: We get one time sum=7 ans two time not,

_7 _ _ 

so, there can be 3 cases, 3*(1/6)*(5/6)*(5/6)

Case-2: We get two time sum=7 ans one time not,

_7 _7  _ 

so, there can be 3 cases, 3*(1/6)*(1/6)*(5/6)

Case-3

We get 7 at all positions,

_7 _7 _7 

and this is only one case, 1*(1/6)*(1/6)*(1/6)

Now, these all are 'OR' cases so  add them,

3*(1/6)(5/6)(5/6)+3*(1/6)(1/6)(5/6)+(1/6)(1/6)(1/6)

=75+15+1/216

= 91/216

P.S. This is just a binomial method only, but in GATE during the process of solving questions remembering formulas can be hard and we solve all the questions iteratively like I did here.

0 votes
0 votes
Trying brute fore method

when the die is tossed once ,probability of getting sum of 7 is 0

when the die is tossed 2 times,probability of getting sum of 7 is 6/36

when the die is tossed 3 times,probability of getting sum of 7 is 15/216

so total probability is (0+6/36+15/216)=51/216
0 votes
0 votes

$P(X) = {N\choose x}* p ^{x} * (1 - p) ^ {x}$

Let X = Probability of getting a total of at least 7

N = 3, Getting 7 ={ (1,6), (6, 1), (2,5), (5, 2), (3, 4), (4, 3) }

                          = p = 6/ 36

$\therefore$ ( 1 – p ) = 30 / 36                                     

 i.e P(X $\geq$ X) = 1 – P(X < 1)

                             = 1 – ${3\choose 0}* ( 6 / 36 ) ^{0 } * (30 / 36 ) ^ {3}$

                             = 1 – ${30 ^ 3} / 36^3$

                              = $46656 – 27000 /  46656$

                              = $19656 / 46656 $

                              = 0.42129

Option a) 125 / 216 = 0.5787

Option b) 91 / 216 = 0.42129

Option c) 117 / 216 = 0.5416

Option d) 9 / 216 = 0.04166

 

Clearly Option b) is correct

Related questions

0 votes
0 votes
1 answer
3
Balaji Jegan asked Oct 23, 2018
239 views
0 votes
0 votes
0 answers
4
Debargha Mitra Roy asked Sep 26, 2023
175 views
Determine the geometric distribution for which the mean is 3 and variance is 4.