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in Introduction to Probability Theory by (47.8k points)
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If m is a number such that m ≤ 5, then the probability that quadratic equation 2x2 + 2mx + m + 1 = 0 has real roots is ...

(a) 1/5

(b) 2/5

(c) 3/5

(d) 4/5

1 Answer

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Best answer

(c) 3/5

2x2 + 2mx + m + 1 = 0

Roots are real ⇒ m2 – 2m – 2 ≥ 0 

Here m ≤ 5 ⇒ n(S) = 5 

When m = 1, m2 – 2m – 2 

When m = 2, m2 – 2m - 2 

When m = 3, m2 – 2m – 2 

When m = 4, m2 – 2n - 2 

When m = 5, m2 – 2m – 2 

⇒ n{A) = 3 and so P(A) = 3/5

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