Q. 2.6 Let E, F, and G be three events.... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 2: Q. 2.6 (page 52)

Let E, F, and G be three events. Find expressions for the events so that, of E, F, and G,
(a) only E occurs;
(b) both E and G, but not F, occur;
(c) at least one of the events occurs;
(d) at least two of the events occur;
(e) all three events occur;
(f) none of the events occurs;
(g) at most one of the events occurs;
(h) at most two of the events occur;
(i) exactly two of the events occur;
(j) at most three of the events occur.

Short Answer

Expert verified

The events are as follows

(a) $E F G$

(b) $E F G$

(d) $E F 鈭� E G 鈭� F G$

(e) $E F G$

(f) $E F G$

(g)role="math" localid="1650438439004" $E F G 鈭� E F G 鈭� E F G 鈭� E F G$

(h) $(E F G)$

(i) $E F G + E F G + E F G$

(j) $S$

Step by step solution

Given information

Three events $E, F and G$

Part(a)

Only E occours $= E F G$

Part(b)

Both E and G occors but not F $= E F G$

Part(c)

Atleast one of the events occor $= E 鈭� F 鈭� G$

Part(d)

Atleast two of the events occor $= E F 鈭� F G 鈭� E G$

Part(e)

All three events occor $= E F G$

Part(f)

None of the events occor $= E F G$

Part(g)

Atmost one of the two events occor $= E F G 鈭� E F G 鈭� E F G 鈭� E F G$

Part(h)

Atmost two of the events occor $= (E F G)$

Part(i)

Exactly two of the events occor $= E F G + E F G + E F G$

Part(j)

Atmost three of the events occor $= S$

where Sdenotes a super-set of all the sets possible.

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Course	Choices
Entree	Chicken or roast beef
Starch	Pasta or rice or potatoes
Dessert	Ice cream or Jello or apple pie or a peach

91影视

Short Answer

Step by step solution

Given information

Part(a)

Part(b)

Part(c)

Part(d)

Part(e)

Part(f)

Part(g)

Part(h)

Part(i)

Part(j)

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