Thank you very much for your help.

Now I see how to work it out properly.

As you say, the probability of success is not constant, so we need to change the probability every time you deal a card.

So, the probability of getting a spade is 13/52, but after that, the total number of cards and the number of spades get one less each time, so the probability of getting a spade five times in a row would be (13/52)*(12/51)*(11/50)*(10/49)*(9/48).

Then, after that, a failure must follow 5 times in a row, so similarly the probability of NOT getting a spade (i.e. getting a non-spade card) 5 times in a row would be:

(39/47)*(38/46)*(37/45)*(36/44)*(35/43).

So, the probability of getting a spade 5 times in a row and then getting a non-spade 5 times in a row would be:

(13/52)*(12/51)*(11/50)*(10/49)*(9/48)

*(39/47)*(38/46)*(37/45)*(36/44)*(35/43)

However, there are (10C5) different ways of getting spades or non-spades, for example,

1 2 3 4 5 6 7 8 9 10

S S S S S F F F F F

F S F F S S F S F S

..........

So it has to be multiplied by 10C5, correct?

Therefore, a correct working and answer would be:

(13/52)*(12/51)*(11/50)*(10/49)*(9/48)*(39/47)*(38/46)*(37/45)*(36/44)*(35/43)

*(10C5) = 0.0468393... is approximately 4.7% (2 s.f.), which is less than 5%.

Thank you very much again for your kind help.

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