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The table gives a set of outcomes and their probabilities. Let
A be the event "the outcome is prime", Let
B be the event "the outcome is less than 4 ". Find
P(A∣B).

Outcome
Probability

1
0.1

2
0.2

3
0.2

4
0.5

◻
Subm:

The table gives a set of outcomes and their probabilities. Let $A$ be the event

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Identify independent events

Full solution

Q. The table gives a set of outcomes and their probabilities. Let

A

be the event

List Prime Numbers: List out the prime numbers from the outcomes given: $2$ and $3$ are prime.
Identify Outcomes Less Than $4$ : Identify the outcomes that are less than $4$ : $1$ , $2$ , and $3$ .
Calculate $P(A \text{ and } B)$ : Calculate $P(A \text{ and } B)$ by adding the probabilities of the outcomes that are both prime and less than $4$ : $P(2) + P(3) = 0.2 + 0.2$ .
Calculate $P(B)$ : $P(A \text{ and } B) = 0.2 + 0.2 = 0.4$ .
Use Formula for $P(A\mid B)$ : Calculate $P(B)$ by adding the probabilities of the outcomes that are less than $4$ : $P(1) + P(2) + P(3) = 0.1 + 0.2 + 0.2$ .
Use Formula for P(AA&# $8745$ ;B): Calculate $P(B)$ by adding the probabilities of the outcomes that are less than $4$ : $P(1) + P(2) + P(3) = 0.1 + 0.2 + 0.2$ . $P(B) = 0.1 + 0.2 + 0.2 = 0.5$ .
Use Formula for P(AA&# $8745$ ;B): Calculate P(B) by adding the probabilities of the outcomes that are less than $4$ : $P(1) + P(2) + P(3) = 0.1 + 0.2 + 0.2$ . $P(B) = 0.1 + 0.2 + 0.2 = 0.5$ .Use the formula $P(A∩B) = \frac{P(A \text{ and } B)}{P(B)}$ to find $P(A∩B)$ .
Use Formula for P(AA&# $8745$ ;B): Calculate $P(B)$ by adding the probabilities of the outcomes that are less than $4$ : $P(1) + P(2) + P(3) = 0.1 + 0.2 + 0.2$ . $P(B) = 0.1 + 0.2 + 0.2 = 0.5$ . Use the formula $P(A∩B) = \frac{P(A \text{ and } B)}{P(B)}$ to find $P(A∩B)$ . $P(A∩B) = \frac{0.4}{0.5} = 0.8$ .

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