**The probabilities of the independent events A and B are 0.4 and 0.5 respectively. Find the following probabilities:**

**a) The probability of A and B occurring.**

**b) The probability of A but not B occurring.**

**c) The probability of A or B occurring.**

**d) The probability of A or not B occurring.**

**e) The probability of A occurring given that B has occurred.**

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**f) The probability of A occurring given that B has not occurred.**

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