A two-different-digit number is needed to be formed from the set of numbers . Determine the probability of the event of having a number whose units and tens digits are odd numbers.

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Example

A two-different-digit number is needed to be formed from the set of numbers . Determine the probability of the event of having a number whose units and tens digits are odd numbers.

Solution

The probability of event occurring is equal to the number of
favorable outcomes divided by the total number of possible
outcomes in the sample space, . In this case, event is
forming a two-digit number from the set of numbers
, where the two digits are different, and the units
and tens digits are odd numbers.

Given that a two-digit number will be formed from the set of
numbers , where the two digits are different, the
sample space contains the following numbers: 35, 37, 38, 39, 53,
57, 58, 59, 73, 75, 78, 79, 83, 85, 87, 89, 93, 95, 97, and 98. Of
these numbers, the ones that have an odd number for the units
digit and the tens digit are 35, 37, 39, 53, 57, 59, 73, 75, 79,
93, 95, and 97, so these are the favorable outcomes for event .
Find the probability of event as follows:

Thus, the probability of forming a number whose units and tens
digits are odd numbers is .