F.5 math probability-----

用戶36732

2011-02-22 12:17 am

Two fair dice are rolled once.Let A be the event that the product of the numbers obtained is a prime number.Let B be the event that the product of the numbers obtained is a composite number. (a) Find P (A∩B)(b) Are A and B mutually exclusive events? Explain briefly.(c) Find P (A U B)(d)Are A and B complementary exclusive events? Explain briefly.

回答 (1)

良師益友

2011-03-04 12:06 am

✔ 最佳答案

Prime numbers are 2, 3, 5, 7 and 11

Composite numbers are 4, 6, 8, 9, 10, 12

The answers are thus as follows:

(a) A and B have no common element

Hence, P( A and B ) = 0

(b) A and B are mutually exclusive as they cannot be happened at the same without common elements.

(c) P( A or B ) = P( A ) + P( B ) - P( A and B )

= P( A ) + P( B )

= P( A sum from 2 to 12 )

= 1

(d) A and B are complementary events since they have no common elements and their total sum is 1.

Hope I can help you.

參考: Mathematics Teacher Mr. Ip

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