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Topic: Probability

Difficulty: 7/10

Hint in 3…..

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Label the 2 prince as A & B, the 2 princesses as 1 & 2.

It is possible to have both prince choosing the same princess and the other way round as well.

Since this question is quite tricky, I will give another hint.

This question is similar to throwing 2 dice and finding out the probability that both will have the same number.

Solution in 3…..

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FULL SOLUTION

Step 1:Since we can relate this to throwing 2 dice, we need to find out the number of outcomes possible in each die. In this scenario, there can be 4 outcomes.

For Prince
1)A1B1(Both Prince choosing Princess 1)
2)A1B2( A chooses 1 & B chooses 2)
3)A2B1
4)A2B2

For Princess
1)1A2A(Both Princess choosing Prince A)
2)1A2B( 1 chooses A & 2 chooses B)
3)2A1B
4)1B2B

Step 2: Since there can be 6×6=36 outcomes from throwing 2 dice, there is 4×4=16 outcomes possible in this question. (1,1) up till (4,4)

Step 3:Out of the 16 outcomes, only 2 outcomes(2,2) & (3,3) will represent both parties choosing each other: Hence the answer is 2/16 = 0.125