Two dice are thrown, 1 is the event that the sum of their dots is a prime number and 2 is the event that 5 is the dot on
the top of second die. Check whether (1 ∩ 2) =
(1). (2)

Given:

Two dice are thrown.

is the event that the sum of their dots is a prime number

is the event that 5 is the dot on the top of second die.

To find:

Whether is true or false.

Solution:

If two dice thrown, then the total possible outcomes are:

(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).

is the event that the sum of their dots is a prime number.

is the event that 5 is the dot on the top of second die.

The intersection of these two events is:

Now,

Therefore, the given statement is false because .

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step-by-step explanation: