Calculating Conditional Probability

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Q1. The Venn diagram shows that in a building with 123 offices, 72 offices have computers in them. 45 offices have windows to the outside of the building. 23 offices have computers and windows. If one office is chosen at random, determine each of the following probabilities written as a fraction in lowest terms.

Conditional Probability:

The conditional probability of an event B in relation to an event A is the probability that event B will occur given that event A has already occurred. The notation used for conditional probability is P(B│A), which is read as "the probability of B given A".

Conditional probability can be determined by two methods:

1. Reducing the sample space outright
2. Using a formula to guide the counting and reasoning

The probability of an event B occurring given that event A has already occurred is given by the formula:

Q2. Determine the following probabilities correct to two decimal places as needed.