Meyer rolls two fair, ordinary dice with the numbers 1,2,3,4,5,6on their sides. What is the probability that at least one of the dice shows a square number?
The only way for Meyer not to roll at least one square number is for non-square numbers to come up on both dice.
Two of the numbers on each die are squares: namely, 1 and 4. Four numbers on each die are not squares:2 , 3, 5, and 6. Thus there are 4*4 =16 ways for Meyer to roll a non-square number on each die, out of 36 equally likely outcomes for the pair of dice. The other 36-16 =20 outcomes each involve a square number showing on one or both dice. So, Meyer's probability of rolling at least one square number is 5/9.
Mary has six cards whose front sides show the numbers 1,2,3,4,5 and 6. She turns the cards face-down, shuffles the cards until their order is random, then pulls the top two cards off the deck. What is the probability that at least one of those two cards shows a square number?
Explain your solution. Is the answer the same as in part (a), or is it different? Why?
probability of a square number is 2/6 = 1/3
probability of not a square is 4/6 = 2/3
at least one die shows a square number is
S = square number
N = not a square number
SS = (1/3)^2
SN = (1/3)(2/3)
NS = (2/3)(1/3)
NN = (2/3)^2
so at least one would be (SS + SN + NS) = 1/9 + 2/9 + 2/9 = 5/9
or everything but NN (1 - NN) = 1 - 4/9 = 5/9 welcomes!