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In this lesson, we will learn how to compute probabilities using Bayes's rule.

Q1:

Suppose that π΄ and π΅ are events with probabilities π ( π΄ ) = 0 . 6 3 and π ( π΅ ) = 0 . 7 7 . Given that π ( π΅ | π΄ ) = 0 . 8 8 , find π ( π΄ | π΅ ) .

Q2:

Suppose that π΄ and π΅ are events in a random experiment. Given that π ( π΄ ) = 0 . 3 9 and π ( π΅ | π΄ ) = 0 . 8 8 , find π ( π΅ β£ π΄ ) β² .

Q3:

Sameh rolls two fair dice numbered from one to six and records the results. Let π΄ be the event of rolling two numbers whose product is a square number and let π΅ be the event of rolling two numbers that are even.

Determine the probability of π΄ .

Determine the probability of π΅ .

Determine the probability of ( π΄ β£ π΅ ).

Determine the probability of ( π΅ β£ π΄ ) .

Is it true that π ( π΄ ) π ( π΅ β£ π΄ ) = π ( π΄ β© π΅ ) and π ( π΅ ) π ( π΄ β£ π΅ ) = π ( π΄ β© π΅ ) ?

Q4:

Suppose that π΄ and π΅ are events with probabilities π ( π΄ ) = 0 . 4 5 and π ( π΅ ) = 0 . 7 . Given that π ( π΅ | π΄ ) = 0 . 8 4 , find π ( π΄ | π΅ ) .

Q5:

Suppose that π΄ and π΅ are events with probabilities π ( π΄ ) = 0 . 4 and π ( π΅ ) = 0 . 6 . Given that π ( π΅ | π΄ ) = 0 . 7 2 , find π ( π΄ | π΅ ) .

Q6:

Suppose that π΄ and π΅ are events in a random experiment. Given that π ( π΄ ) = 0 . 3 6 and π ( π΅ | π΄ ) = 0 . 7 5 , find π ( π΅ β£ π΄ ) β² .

Q7:

Suppose that π΄ and π΅ are events in a random experiment. Given that π ( π΄ ) = 0 . 4 5 and π ( π΅ | π΄ ) = 0 . 6 6 , find π ( π΅ β£ π΄ ) β² .

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