In the two dice experiment, if E is the even of getting the sum of numbers on dice as 11 and F is the event of getting a number other than 5 on the first die. find P (E and F). Are E and F independent events?

Solution

Total number of outcomes = 6 × 6 = 36
Number of outcomes favourable to E = 2. [i.e., (5, 6), (6, 5)]
Let F be the event that the number 5 does not appear on the first die.
Number of outcomes favourable to F = 30
Now, $straight P left parenthesis straight E right parenthesis space equals space 2 over 36 space equals space 1 over 18 comma space space straight P left parenthesis straight F right parenthesis space equals space 30 over 36 space equals space 5 over 6$
$straight P left parenthesis straight E intersection straight F right parenthesis space equals space 1 over 36 not equal to 1 over 18 cross times 5 over 6 space equals space straight P left parenthesis straight E right parenthesis space cross times straight P left parenthesis straight F right parenthesis$
Therefore, E and F are not independent events.

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Probability

In the two dice experiment, if E is the even of getting the sum of numbers on dice as 11 and F is the event of getting a number other than 5 on the first die. find P (E and F). Are E and F independent events?

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