Question

two fair dice are rolled simultaneously 67 times .a doublet is obtained 8 times now if the pair of dice are rolled simultaneously again at random what is the probability of getting a doublet and probability of not getting a doublet​

Answer 1

Answer:

no. of times a doublet is obtained = 8

no. of times dices are rolled = 67

therefore p(getting a doublet) = 8/67

p( not getting a doublet ) 59/67

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Answer 2

Given:

The number of dice rolled simultaneously = 2.

To Find:

We have to find the probability of getting a doublet and the probability of not getting a doublet if the pair of dice are rolled simultaneously at random.

Solution:

The total number of cases on rolling a pair of dice = 6 × 6 = 36.

The possible doublets in pairs of dice = (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6).

The number of doublets = 6.

Probability of getting a doublet = $\frac{Number of possible events}{Total number of events} = \frac{6}{36} = \frac{1}{6}.$

Total probability of any event is 1.

∴, Probability of not getting a doublet = $1 -$  Probability of getting a doublet

$= 1-\frac{1}{6} = \frac{5}{6}.$

Hence, the probability of getting a doublet and the probability of not getting a doublet are $\frac{1}{6}$ and $\frac{5}{6}$, respectively.

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