Mathematics: 6. e1 and e2 are events from the same sample space; p(e1)=0.37, p(e2)=0.45, and p(e1, e2)=0.14. a. find the probability that e2 does not occur. b. find the probability that either e1 or e2 occurs. c. find the probability that neither e1 nor e2 occurs.

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6. e1 and e2 are events from the same sample space;

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12.01.2022

a. 0.55

b. 0.68

c. 0.18

Step-by-step explanation:

a. The probability that E2 does not occur is one minus the probability that E2 occurs:

$1-P(E2)= 1- 0.45\\1-P(E2) = 0.55$

b. The probability that either E1 or E2 occurs is given by the sum of their individual probabilities minus their joint probability:

$P(E1\ or\ E2) = P(E1)+P(E2)-P(E1, E2)\\P(E1\ or\ E2)=0.37+0.45-0.14\\P(E1\ or\ E2)=0.68$

c. The probability that neither E1 nor E2 occurs is one minus the probability of E1 occurring minus the probability of E2 occurring:

$1-P(E1)-P(E2)= 1- 0.37 -0.45\\1-P(E1)-P(E2) = 0.18$

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