An experiment involves tossing a single balanced, six-sided die. These are some

Question

An experiment involves tossing a single balanced, six-sided die. These are some events A: Observe a 1 B: Observe an odd number C: Observe a number greater than 1 D: Observe both A and B E: Observe A or B or both F: Observe both A and C (a) List the simple events in the sample space (b) List the simple events in each of the events A through F. (If an event has no simple events, enter NONE.) event A event B event C event event E event F (c) What probability should you assign to each of the simple events? (Enter your probability as a fraction.) (d) Calculate the probabilities of the six events A through F by adding the appropriate simple-event probabilities. (Enter your probabilities as fractions.) P(A) = P(B) = P(C) = P(D) = P(E) = P(F) =

Explanation / Answer

Solution:-

a) {1, 2, 3, 4, 5, 6}

b) A : {1}

B : {1, 3, 5}

C : {2, 3, 4, 5, 6}

D : {1}

E : {1, 3, 5}

F : {NONE}

c) 1/6

d) A = 1/6

B = 3/6 = 1/2

C = 5/6

D = 1/6

E = 3/6 = 1/6

F = 0

2).

a)

P(E1) + P(E2) + P(E3) + P(E4) + P(E5) = 1

0.25 + 0.25 + 0.35 + 2P(E5) + P(E5) = 1

0.85 + 3P(E5) = 1

P(E5) = 0.15 / 3 = 0.05

Therefore, P(E4) = 2 * 0.05 = 0.10 and P(E5) = 0.05

b) A = 0.25 + 0.35 + 0.10 = 0.70

B = 0.25 + 0.35 = 0.55

c) {E1, E2, E3, E4}

d) {E3}

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