There are 10 balls in a box. 2 of them are red and the other 8...
There are 10 balls in a box. 2 of them are red and the other 8 are white.
John draws one ball randomly from the box.
Then Emily draw another ball randomly from the remaining 9 balls.
Let E be the event that John draws a red ball.
Let F be the event that Emily draws a red ball.
(i) Write out P(E), P(F|E), P(F|EC) directly.
(ii) Find out P(F). (Hint: Apply the law of total probability) Suppose that they can win prizes if they have a red ball. Is it a fair game for John and Emily, in other words, does the order of drawing matter?
(iii) Find out P(EF). Are E and F independent? Think and comment on the relationship between independence and fair.
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