Question

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting: (a) at least 1 nun? (b) exactly 0 nuns? (c) exactly 0 hei? (d) at most 1 gimels?

Answer 1

a) Probability of getting at least 1 nun

= 1 - Probability that we got non nun in all three spins

= 1 - (3/4)³

= 1 - (27/64)

= 0.578125

Therefore 0.578125 is the required probability here.

b) Probability of exactly 0 nuns is computed here as:

= 1 - Probability of at least 1 nun

= 1 - 0.578125

= 0.421875

Therefore 0.421875 is the required probability here.

c) Due to symmetry, as we know here that:
P( nun) = P(hei)

Therefore 0.421875 is the required probability here.

d) P( at most 1 gimels ) is computed here as:

= P( 0 gimels ) + P( 1 gimel)

= 0.75³ + 3*0.25*0.75²

= 0.84375

Therefore 0.84375 is the required probability here.