Two marbles are drawn randomly one after the other without replacement from a jar that contains 4 red marbles, 3 white marbles, and 8 yellow marbles. Find the probability of the following events. Give your answers to at least 4 decimal places, or as an exact expression.

(a) A red marble is drawn first followed by a white marble.

The probability is

(b) A white marble is drawn first followed by a white marble.

The probability is :

(c) A yellow marble is not drawn at all.

The probability is :

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"Channel One" is an educational television network for which participating secondary schools are equipped with TV sets in every classroom. It has been found that 35% of secondary schools subscribe to Channel One, where of these subscribers 20 % never use Channel One while 30% claim to use it more than 5 times per week.

Find the probability that a randomly selected secondary school subscribes to Channel One and uses it more than 5 times per week.

Write out each of the 3 probabilities you've been given in probability notation. 2 of them are conditional probabilities.

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A quick quiz consists of 5 multiple choice problems, each of which has 5 answers, only one of which is correct. If you make random guesses on all 5 problems,

(a)

What is the probability that all 5 of your answers are incorrect?

answer:

(b)

What is the probability that all 5 of your answers are correct?

answer:

Give your answers to at least 4 decimal places, or as an exact expression.

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A card is drawn from a regular deck of 52 cards and is then put back in the deck. A second card is drawn. What is the probability that:

(a) The first card is red.

(b) The second card is hearts given that the first is red.

(c) The first card is red and the second is hearts