Question

Events A, B, and C are independent. P(A) = 0.15 P(B) = 0.3 P(C) = 0.4

a) probability that all events occur

b) Probability that at least one occurs

c) Probability that none occurs

d) Probability that exactly one event occurs

Answer #1

Given:-

Events A, B, and C are independent.

P(A) = 0.15 P(B) = 0.3 P(C) = 0.4

**a) probability that all events occur?**

Probability that all events occur = P(A and B and C) = P(A) * P(B) * P(C)

= 0.15 * 0.3 * 0.4

= 0.018

**b) Probability that at least one occurs?**

Probability that at least one occurs = P(A) + P(B) + P(C) - P(A and B and C)

= 0.15 + 0.3 + 0.4 - 0.018

= 0.832

**c) Probability that none occurs?**

Probability that none occurs = 1 - P(A and B and C)

= 1 - 0.018

= 0.982

**d) Probability that exactly one event
occurs?**

Probability that exactly one event occurs:-

13.
Assume A and B are independent events with P(A)= 0.2 and P(B)= 0.3.
let C be the event that none of the events A and B occurs, let D be
the event that exactly one of the events A and B occurs. Find P(A
given D)?

1. Suppose that A, B are two independent events, with
P(A) = 0.3 and P(B) = 0.4.
Find P(A and B)
a. 0.12
b. 0.3
c. 0.4
d. 0.70
2. Experiment: choosing a single ball from a bag which
has equal number of red, green, blue, and white ball and then
rolling a fair 6-sided die.
a.) List the sample space.
b.) What is the probability of drawing a green ball and
even number?
2.

Let P(A) = 0.1, P(B) = 0.2, P(C) = 0.3 and P(D) = 0.4;
A, B, C, D – independent events. Compute P{(A∪B)∩ (Cc ∪
Dc }.
Step by step solution.

For each situation, determine if events A, B are independent.
Explain.
P(A | B) = 0.4,
P(B) = 0.8, and P(A) =
0.5
P(A | B) = 0.3,
P(B) = 0.8, and P(A) =
0.3
P(A) = 0.2, P(B) =
0.2, and A and B are mutually
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Suppose P(A) = 0.60, P(B) = 0.85, and A and B are independent. The
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(a) 0.4 x 0.15 = 0.060
(b) 0.4 + 0.15 0.060
(c) 1-(0.40 + 0.15) = 0.45
(d) 1- (0.6 x 0.85) = 0.490

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Let A and B be two events from the sample space S. Given
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e) P(not(A or B))

Events A and B are independent. Suppose event A occurs with
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Compute the probability that A occurs or B does not occur (or
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MC0402: Suppose there are two events, A and B.
The probability of event A is P(A) = 0.3.
The probability of event B is P(B) = 0.4.
The probability of event A and B (both occurring) is P(A and B)
= 0.
Events A and B are:
a.
40%
b.
44%
c.
56%
d.
60%
e.
None of these
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Complementary events
b.
The entire sample space
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d.
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e.
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Events A and B are independent. Suppose event
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Compute the probability that B occurs but A
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Compute the probability that either A occurs without
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