Each participant in an experiment was given one of three tasks. Let these three tasks be symbolized by A1,A2, A3 . The number of errors each participant made in performing the task was recorded by use of the categories “0 errors,” “1 error,” and “2 or more errors.” Thus, every participant was classified in two ways, by task and by number of errors. The following table shows the probabilities for these joint events for any participant drawn at random. Task   Errors A1 A2 A3 Total 0 .05 .02 .13 .20 1 .08 .17 .10 .35 2 or more .20 .15 .10 .45 Total .33 .34 .33 Use these probabilities to find: The marginal probabilities of the task events A1,A2, A3 The marginal probabilities for numbers of errors The conditional probability for zero errors given task A1 The conditional probability for two or more errors given task A2 The conditional probability of task A3 given no errors

Each participant in an experiment was given one of three tasks. Let these three tasks be symbolized by A_1,A_2, A₃ . The number of errors each participant made in performing the task was recorded by use of the categories “0 errors,” “1 error,” and “2 or more errors.” Thus, every participant was classified in two ways, by task and by number of errors. The following table shows the probabilities for these joint events for any participant drawn at random.

Total .33 .34 .33

Use these probabilities to find:

• The marginal probabilities of the task events A_1,A_2, A₃
• The marginal probabilities for numbers of errors
• The conditional probability for zero errors given task A₁
• The conditional probability for two or more errors given task A₂
• The conditional probability of task A₃ given no errors