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  4. Two dice are thrown and two coins are tossed simultaneously. The probability of getting prime numbers on both the dice along with a head and a tail on the two coins is

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Q. Two dice are thrown and two coins are tossed simultaneously. The probability of getting prime numbers on both the dice along with a head and a tail on the two coins is

TS EAMCET 2018

Solution:

Since number of getting prime numbers $\{2,3,5\}$ is 3 therefore number of getting prime numbers on both the dice is $3 \times 3$.
And getting a head and a tail on two coins $=1 \times 1 \times 2$
And total number of possibilities $=(6 \times 6) \times(2 \times 2)$
So, required probability $=\frac{3 \times 3 \times 1 \times 1 \times 2}{16 \times 6 \times 2 \times 2}=\frac{1}{8}$