perplexus.info :: Probability : Real roots from three dice

Real roots from three dice (Posted on 2016-09-20)

Die 1 is an unbiased and regular six-sided die numbered 1 to 6.
Die 2 is an unbiased and regular seven-sided die numbered 2 to 8.
Die 3 is an unbiased and regular eight sided die numbered 3 to 10

Consider the quadratic equation Ax²+Bx+C= 0.

We assign values to the coefficient A by throwing Die 1, the coefficient B by throwing Die 2 and the coefficient C by throwing Die 3.

Determine the probability that the equation will have real roots.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer-aided solution

Comment 1 of 1

There are 52 cases of real roots out of the 336 possible combinations that are possible. (5 of the 52 cases are examples of double real roots)

The probability is therefore 52/336 = 13/84 ~= 0.154761904761905.

Private Sub Form_Load()

Form1.Visible = True

Text1.Text = ""

crlf = Chr$(13) + Chr$(10)

For a = 1 To 6

For b = 2 To 8

For c = 3 To 10

disc = b * b - 4 * a * c

If disc >= 0 Then

If disc = 0 Then dblCt = dblCt + 1

realCt = realCt + 1

End If

ct = ct + 1

Text1.Text = Text1.Text & crlf & realCt & Str(ct) & " " & "(" & dblCt & ")"

Text1.Text = Text1.Text & crlf & realCt / ct & crlf

End Sub

Posted by Charlie on 2016-09-20 15:43:45

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