# Two dice, one blue and one grey, are thrown at the same time.A student argues that-there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.

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Given:

Two dice, one blue and one grey, are thrown at the same time.

A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10,11 and 12. Therefore, each of them has a probability $\frac{1}{11}$.

To do:

We have to find whether the argument of the student is correct or false.

Solution:

When two dice (one blue and one green) are thrown at the same time, the total number of outcomes $=6 \times 6=36$

This implies,

The total number of possible outcomes $n=36$.

When the sum on the two dice $=2$, the possible outcome is $(1,1)$

Number of favorable outcomes $=1$

Probability that the sum on the two dice is 2 $=\frac{1}{36}$

When the sum on the two dice $=3$, the possible outcome is $(1,2), (2,1)$

Number of favorable outcomes $=2$

Probability that the sum on the two dice is 3 $=\frac{2}{36}$

When the sum on the two dice $=4$, the possible outcome is $(1,3), (2,2), (3,1)$

Number of favorable outcomes $=3$

Probability that the sum on the two dice is 4 $=\frac{3}{36}$

When the sum on the two dice $=5$, the possible outcome is $(1,4),(2,3),(3,2),(4,1)$

Number of favorable outcomes $=4$

Probability that the sum on the two dice is 5 $=\frac{4}{36}$

When the sum on the two dice $=6$, the possible outcome is $(1,5),(2,4),(3,3),(4,2),(5,1)$

Number of favorable outcomes $=5$

Probability that the sum on the two dice is 6 $=\frac{5}{36}$

When the sum on the two dice $=7$, the possible outcome is $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$

Number of favorable outcomes $=6$

Probability that the sum on the two dice is 7 $=\frac{6}{36}$

When the sum on the two dice $=8$, the possible outcome is $(2,6),(3,5),(4,4),(5,3),(6,2)$

Number of favorable outcomes $=5$

Probability that the sum on the two dice is 8 $=\frac{5}{36}$

When the sum on the two dice $=9$, the possible outcome is $(3,6),(4,5),(5,4),(6,3)$

Number of favorable outcomes $=4$

Probability that the sum on the two dice is 9 $=\frac{4}{36}$

When the sum on the two dice $=10$, the possible outcome is $(4,6),(5,5),(6,4)$

Number of favorable outcomes $=3$

Probability that the sum on the two dice is 10 $=\frac{3}{36}$

When the sum on the two dice $=11$, the possible outcome is $(5,6),(6,5)$

Number of favorable outcomes $=2$

Probability that the sum on the two dice is 11 $=\frac{2}{36}$

When the sum on the two dice $=12$, the possible outcome is $(6,6)$

Number of favorable outcomes $=1$

Probability that the sum on the two dice is 12 $=\frac{1}{36}$

No, the outcomes are not equally likely from the above table we see that, there is different probability for different outcomes.

Updated on 10-Oct-2022 13:27:00