# Probability - tree diagram

## Probability - tree diagram

In a factory, three machines, J, K and L, are used to make biscuits.

Machine J makes 25% of the biscuits.

Machine K makes 45% of the biscuits.

The rest of the biscuits are made by machine L.

It is known that 2% of the biscuits made by machine J are broken, 3% of the biscuits made by machine K are broken and 5% of the buiscuits made by machine L are broken.

(a) Draw a tree diagram to illustrate all the possible outcomes and associated probabilities.

A biscuit is selected at random.

(b) Calculate the probability that the buiscuit is made by machine J and is not broken.

(c) Calculate the probability that the biscuit is broken.

(d) Given that the biscuit is broken, find the probability that it was not made by machine K.

Machine J makes 25% of the biscuits.

Machine K makes 45% of the biscuits.

The rest of the biscuits are made by machine L.

It is known that 2% of the biscuits made by machine J are broken, 3% of the biscuits made by machine K are broken and 5% of the buiscuits made by machine L are broken.

(a) Draw a tree diagram to illustrate all the possible outcomes and associated probabilities.

A biscuit is selected at random.

(b) Calculate the probability that the buiscuit is made by machine J and is not broken.

(c) Calculate the probability that the biscuit is broken.

(d) Given that the biscuit is broken, find the probability that it was not made by machine K.

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