Name: Equally Likely Outcomes of an Experiment
Uploaded: 2019-07-19
Duration: 1 min 59 s
Description: In this video, we will understand the concept of equally likely outcomes in probability with the help of some examples. Hit on the play button to know more.

Question

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product of the numbers lies between

8

and

13

Accepted Answer

The total possible outcomes when two dice thrown are given by

$S = (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)$

Thus, total number of possible outcomes $= 36$

Now, the outcomes for which the product of the numbers is between $8$ and $13$ are $\{(5, 2), (6, 2) (3, 3) (3, 4) (2, 5) (2, 6) (4, 3)\}$ .

Let $E$ be the event of getting the product between $8$ and $13$ .Then, number of outcomes favourable to the event $E = 7$ .

Hence, the probability that the product of the numbers lies between $8$ and $13 = \frac{7}{36}$

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product of the numbers lies between $8$ and $13$

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