Any shortcuts? The probability of problem getting solved by X, Y and Z are 1/4, 2/3 and 3/5 respectively.Find out the probability of pr...

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Any shortcuts?

The probability of problem getting solved by X, Y and Z are 1/4, 2/3 and 3/5 respectively.
Find out the probability of problem is solved.

a 0.85

b 0.75

c 0.70

d 0.90

 

1 Replies

  • Replied 1 year ago

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    Any one of them or two of them or all of them can solve the problem
    For X to solve – 1/4 so, not solve – 3/4
    For Y to solve – 2/3 so, not solve – 1/3
    For Z to solve – 3/5 so, not solve – 2/5
    So, the required probability is = solved by only x + solved by only y + solved by only z + solved by x and z + solved by y and z + solved by x and z + solved by x, y and z
    = 1/4 * 1/3*2/5 + 2/3*3/4*2/5 + 3/4*1/3*3*5 + 3/4*1/3 * 3*5 + 2/3*3/5*3/4 + 1/4*3/5*1/3+1/4*2/3*3/5
    = 2/60 + 12/60 + 9/60 + 9/60 + 12/60 + 3/60+6/60
    = 51/60 = 17/20 = 0.85

Probability · CATKing Forum

Any shortcuts? The probability of problem getting solved by X, Y and Z are 1/4, 2/3 and 3/5 respectively.Find out the probability of pr...

Body

Any shortcuts?

The probability of problem getting solved by X, Y and Z are 1/4, 2/3 and 3/5 respectively.
Find out the probability of problem is solved.

a 0.85

b 0.75

c 0.70

d 0.90

 

1 Replies

  • Replied 1 year ago

    Report

    Any one of them or two of them or all of them can solve the problem
    For X to solve – 1/4 so, not solve – 3/4
    For Y to solve – 2/3 so, not solve – 1/3
    For Z to solve – 3/5 so, not solve – 2/5
    So, the required probability is = solved by only x + solved by only y + solved by only z + solved by x and z + solved by y and z + solved by x and z + solved by x, y and z
    = 1/4 * 1/3*2/5 + 2/3*3/4*2/5 + 3/4*1/3*3*5 + 3/4*1/3 * 3*5 + 2/3*3/5*3/4 + 1/4*3/5*1/3+1/4*2/3*3/5
    = 2/60 + 12/60 + 9/60 + 9/60 + 12/60 + 3/60+6/60
    = 51/60 = 17/20 = 0.85