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CMI2011-A-02

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You have two six-sided cubic dice but they are numbered in a strange manner. On the first die, two opposite faces are numbered $1$, two opposite faces are numbered $3$ and the last pair of opposite faces are numbered $6$. On the second die, the three pairs of opposing faces are numbered $2$, $4$ and $5$. Both dice are fair: each side has an equal probability of coming face up when tossed. Which of the following statements is not true of this pair of unusual dice?

  1. The probability that the sum of the values shown by the dice is $5$ is the same as probability that the sum is $8$.
  2. The probability that the sum is odd is higher than the probability that the sum is even.
  3. The probability that the sum is strictly less than $7$ is the same as the probability that the sum is strictly greater than $7$.
  4. The probability that the sum is a multiple of $5$ is the same as the probability that the sum is a prime number.

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favourable outcome for first dice=(1,3,6)

favourable outcome for second dice=(2,4,5)

SUM(X) 3 5 6 7 8 10 11
P(X) 1/9 2/9 1/9 1/9 2/9 1/9 1/9

A) P(X=5)=2/9 and P(X=8)=2/9  so TRUE

B)P(X=ODD(3,5,7,11))=5/9 and P(X=EVEN(6,8,10))=4/9 TRUE

C)P(X<7)=4/9 and P(X>7)=4/9 True

d)P(X=multiple of 5(i.e. 5,10))=3/9 and P(X=prime number(i.e. 3,5,7,11))=5/9 FALSE

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