A dreidl is a four-sided top that contains a Hebrew letter on each side: nun, gi

Question

A dreidl is a four-sided top that contains a Hebrew letter on each side: nun, gimmel, heh, shin. These letters are an acronym for the Hebrew phrase nes gadol hay ah sham (a great miracle happened there), which refers to the miracle of the temple light that burned for eight days with only one day's supply of oil-the miracle celebrated at Chanukah. Here we suppose that a fair dreidl (one that is equally likely to fall on each of its four sides) is to be spun ten times. Compute the probability of each of the following events: Five gimmels and five hehs: No nuns or shins: Two letters are absent and two letters are present: At least two letters are absent.

Explanation / Answer

Firstly, we will find the possible number of out comes = 410 since the driedl is thrown 10 times each having four possible outcomes.

Now,

P ( 5G , 5H ) = 10C5 (1/4)5 (1/4)5

= 63 / 262144

b) No nuns or shins. So here we are reduced to choose from 2 outcomes every time for ten times.

This can be done in 210 ways

Hence, probability = 210 / 410 = 1 / 210

c) Two letters absent and two letters present will be :

4C2 (210 - 2) / 410 = 5.8479 * 10-3

i.e choose 2 of the four alphabets and keep choosing out of those. The 2 is subtracted at the end to adjust for the cases where there are only one of the two alphabets 10 times.

d) At least 2 letter are absent = cases with only 2 letters + cases with only one letter

= 4C2 (210 - 2) / 410 + 4C3 (1) / 410

= 5.8517 * 10-3

Hope this helps, Ask if you have any doubts.

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