You are given 50 white marbles and 50 black marbles along with two jars.
You are asked to place all 100 marbles into the jars in any way you choose.
Afterwards, you will be blindfolded, the jars will be shaken and rearranged, and you will be asked to select just one marble (from either jar).
How would you arrange the marbles originally to maximise the probability of drawing a white marble?
Hint: Splitting the marbles evenly isn't the best approach.
Place one white marble in the first jar and place the remaining 49 white and 50 black marbles in the second jar.
This placement gives a large increase in the chances of drawing a white marble.
The probability of selecting either jar is 0.5, the probability of drawing a white marble from one jar is 1 and from the other jar is 49/99.
Therefore the overall probability is 0.5 x (1) + 0.5 x (49/99) = 0.74747.
From me to you with LOVE: how many times does the word LOVE appear in this grid?
L V E V O L E E V O L E V O L
O O V E O O E V O L L V V O L
V L O V E V V O O O L O V E O
E O L O V E O L V L E L E V V
E V O L E E L E O L E V O L E
V V O L V V O L O V O L O V E
O V O L O O V V O L E L O L E
L V O L L L E L O V E L O V E
E V L O V E V V O L O V E V E
E E L L E V O L O E E V O L E
L V V O L L L V L L V L L L V
L O E V V O E O O E V O L O O
O L V E V E V V V E V O L V L
V O O E L E E E E E L O V E O
E V L E V O L O V E V O L O V
Hint: Try fixing the number of children to see what happens.
With 149 men and 259 women. The best way is to fix the number of children and play around with the numbers of the men and women to see what happens as these are changed. It soon becomes apparent how changing the children changes the answer and 92 is soon found.
Below are five proverbs, however, each letter has been replaced by its position in the alphabet, but the spaces between the resulting numbers have been removed.
Hint: The first words of the proverbs are Like, Like, A, Judge, A.
Like father, like son.
Like mother, like daughter.
A bad penny always turns up.
Judge not, that ye be not judged.
A little learning is a dangerous thing.