# 11.4.1. Calculating Probability

If and are two events of a sample space of a random experiment, where and , find the value of .

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Given that , , and are three mutually exclusive events in a sample space of a random experiment, where , , and , determine .

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40 rats were injected with a poisonous substance, and the number of dead rats is observed within 12 hours. If the probability that at most 24 rats will die is , and the probability that exactly 24 rats will die is , determine the probability that at least 24 rats will die.

- A0.65
- B0.35
- C0.9
- D0.55

Given that is a sample space of a random experiment, where , , , and , determine .

- A0.17
- B0.3
- C0.16
- D0.37

In a store selling computer sets, given that the probability of selling 31 sets at least daily is 0.79, and the probability of selling less than 34 sets is 0.71, determine the probability of selling 31, 32, or 33 sets.

- A0.21
- B0.5
- C0.08
- D0.29

The probability that Adam succeeding mathematics is 0.5, the probability of him failing Physics is 0.44, and the probability of him succeeding in one of them at least is 0.87. Find the probability that Adam succeeding one of the two subjects at most.

- A0.81
- B0.19
- C0.13
- D0.68

The probability that Adam succeeding mathematics is 0.33, the probability of him failing Physics is 0.32, and the probability of him succeeding in one of them at least is 0.71. Find the probability that Adam succeeding ONLY one of the two subjects.

- A0.41
- B0.29
- C0.3
- D0.7

The probability that a student succeeds in mathematics is 0.72, and the probability that he fails in physics is 0.28, while the probability that he succeeds in one of the two subjects at least is 0.76. Determine the probability that he fails in the two subjects.

- A0.24
- B0.32
- C0.08
- D0.68

If and are two events in a sample space of a random experiment, where , , and , determine .

- A0.64
- B0.75
- C0.48
- D0.09

Given that and are two mutually exclusive events in a sample space , and is a probability function on , where , , and , determine the value of .

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A box contains 11 white balls, red ones, and black ones. If a ball is drawn randomly from it, where the probability that the ball is white , and the probability that the ball is red , then the number of the red balls , and the number of the black balls .

- A6, 3
- B3, 6
- C11, 6
- D11, 3

A bag contains 12 balls, where 4 of them carry the number 1, 4 of them carry the number 2, and the remainder carry the number 3. Two balls are drawn randomly one after the other with replacement, then the probability of the two balls carry two numbers whose sum is at least 3 is .

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A ball is randomly drawn from a box that has 17 balls of the same size; 4 are white, 5 are red, and the rest are green. Determine the probability of the ball being red or green.

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If a ball is drawn from a box containing 19 identical marbles; 4 of them are white, 10 are red, and the rest are green, determine the probability of the ball being yellow.

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- D0

A ball is randomly drawn out of a box that has 27 balls of the same size; 10 of them are white, 9 are red, and the rest are green. Determine the probability of the ball NOT being green.

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Given that is an event in a sample space of a random experiment, where , determine .

- A0
- B1
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- D

If and are two events in a sample space of a random experiment, where , , and . Find .

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and are two events in a sample space of a random experiment. Given that , , and , determine .

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If and are two events in a sample space of a random experiment where , , and , determine .

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Given that and are two events in a sample space of a random experiment where , , and , determine .

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and are two events in a sample space of a random experiment. Given that , , and , determine .

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If and are two events in a sample space of a random experiment, where , , and , find .

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Given that and are two events of a random experiment, in which , , and , determine .

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and are two events in a sample space of a random experiment, where , , and . Find .

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and are two events in a sample space of a random experiment, where , , and . Find .

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and are two events in a sample space of a random experiment, where and . Find if .

- A0.7
- B0.47
- C0.31
- D0.93

and are two events in the sample space of a random experiment, where and . Find if and are mutually exclusive events.

- A0.47
- B0.31
- C0.62
- D0.93

and are two events in the sample space of a random experiment, where and . Find if and are mutually exclusive events.

- A0.39
- B0.16
- C0.78
- D0.13

and are two events in the sample space of a random experiment, where and . Find if .

- A0.32
- B0.64
- C0.51
- D0.16

If and are two events of a random experiment, where , , and , determine the probability of occurrence of the event only.

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If and are two events of a random experiment, where , , and , determine the probability of occurrence of one of the two events at least.

- A0.7
- B0.9
- C0.8
- D0.2

If and are two events of a random experiment, where , , and , find the probability of occurrence of one of the two events at most.

- A0.8
- B0.6
- C0.3
- D0.5

If and are two events of a random experiment, in which , , and , determine the probability of occurrence of ONLY one of the two events.

- A0.3
- B0.7
- C0.6
- D0.5

If and are two events of a random experiment, in which , , and , determine the probability of occurrence of ONLY one of the two events.

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If and are two events of a random experiment, where , , and , determine the probability of occurrence of one of the two events at most.

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and are two events in a sample space of a random experiment, where and . Find if and are mutually exclusive events.

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and are two events in the sample space of a random experiment, where and . Find if .

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If the success probability of a student in physics is 0.85, in mathematics is 0.8, and in both subjects is 0.71, find his success probability in at least one of the two subjects.

- A0.09
- B0.94
- C0.14
- D0.85

If the success probability of a student in physics is 0.71, in mathematics is 0.81, and in both subjects is 0.68, find his success probability in mathematics ONLY.

- A0.13
- B0.71
- C0.03
- D0.84

Given that is a sample space of a random experiment, where , , and