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Four cards will be dealt off the top of a well-shuffled deck. There are two options: (i) To win \(\$ 1\) if the first card is a club and the second is a diamond and the third is a heart and the fourth is a spade. (ii) To win \(\$ 1\) if the four cards are of four different suits. Which option is better? Or are they the same? Explain.

A deck of cards is shuffled and the top two cards are placed face down on a table. True or false, and explain: (a) There is 1 chance in 52 for the first card to be the ace of clubs. (b) There is 1 chance in 52 for the second card to be the ace of diamonds. (c) The chance of getting the ace of clubs and then the ace of diamonds. 1\(/ 52 \times 1 / 52\) .

A coin is tossed six times. Two possible sequences of results are (i) HTTHTH (ii) HHHHH (The coin must land \(\mathrm{H}\) or \(\mathrm{T}\) in the order given \(; \mathrm{H}=\) heads \(, \mathrm{T}=\) tails. \()\) Which of the following is correct? Explain. (a) Sequence (i) is more likely. (b) Sequence (ii) is more likely. (c) Both sequences are equally likely.

A die is rolled 10 times. Find the chance of \(-\) (a) getting 10 sixes. (b) not getting 10 sixes. (c) all the rolls showing 5 spots or less.