Chapter 2: Q. 2.11 (page 53)

If $P (E) = . 9$ and $P (F) = . 8$ , show that $P (E F) \geq . 7$ .In general, prove Bonferroni’s inequality, namely $P (E F) \geq P (E) + P (F) - 1$ .

Short Answer

Expert verified

Therefore,

Transform $P (E \cup F) \leq 1$ .

Use the proven inequality to get $P (E F) \geq 0.7$ .

Step by step solution

Given Information.

Given $P (E) = . 9$ and $P (F) = . 8$ .

Explanation.

For any events $E, F$

$P (E) + P (F) - 1 \leq P (E F)$

This is because:

$P (E \cup F) \leq 1 P (E \cup F) = P (E) + P (F) - P (E F) P (E) + P (F) - P (E F) \leq 1 P (E) + P (F) - 1 \leq P (E F)$

So if $P (E) = 0.9$ and $P (F) = 0.8$ .

$P (E F) \geq P (E) + P (F) - 1 = 0.9 + 0.8 - 1 = 0.7$

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If $P (E) = . 9$ and $P (F) = . 8$ , show that $P (E F) \geq . 7$ .In general, prove Bonferroni’s inequality, namely $P (E F) \geq P (E) + P (F) - 1$ .

Short Answer

Step by step solution

Given Information.

Explanation.

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If P(E)=.9andP(F)=.8, show thatP(EF)≥.7.In general, prove Bonferroni’s inequality, namelyP(EF)≥P(E)+P(F)−1.

Short Answer

Step by step solution

Given Information.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Decision Maths

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

If $P (E) = . 9$ and $P (F) = . 8$ , show that $P (E F) \geq . 7$ .In general, prove Bonferroni’s inequality, namely $P (E F) \geq P (E) + P (F) - 1$ .