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SCMP Reporter

Two events are independent if the occurrence or non-occurrence of one event does not affect the probability of occurrence of the other event.

1. Two fair dice, one green and one red, are thrown.

Let A be the event that the green die is even.

Let B be the event that the red die is greater than 4.

(a) Find P (A) and P (B).

P (A) = 1/2

P (B) = 1/3

(b) Find the probability that both A and B happen.

P (green die is even and red die is greater than 4):

= 6/36   =   1/6

(c) What can you say about P (A), P (B) and P (A and B)?

If A and B are independent events, then

P (A and B)  =  P (A) P (B)

2. In tossing a coin twice, what is the probability that both are heads?

P (1st toss is H) = 1/2

P (2nd toss is H) = 1/2

P (both are H) = (1/2) (1/2)  =  1/4

3. A bag contains 3 white balls and 4 black balls. Two balls are drawn in succession from the bag. The first ball is replaced before the next one is drawn.

Let A be the event that the first ball drawn is white.

Let B be the event that the second ball drawn is black.

(a) Find P (A) and P (B)

P (A)  =  3/7

P (B)  =  4/7

(b) Find the probability that the first ball drawn is white and the second ball drawn is black.

P (A and B)  =  12/49

Product law

If E and F are independent events, then:

P (E and F)  =  P (E) P (F)

1. In a multiple-choice test, each question has five choices. If a student attempts each question by guessing, find the probability that:

(a) he will answer the first four questions correctly.

P (first four questions correct):

=  (1/5) (1/5) (1/5) (1/5)  =  1/625

(b) he will answer the first question correctly and the next

three wrongly.

P (first one correct and next three wrong):

=  (1/5) (4/5) (4/5) (4/5)

=  64/625

2. Two cards are drawn in succession from a deck of 52 cards. The first card is replaced after the first draw. Find the probability that:

(a) both are the king of spades.

P (first card is king of spades)  =  1/52

P (second card is king of spades)  =  1/52

P (both are king of spades) = (1/52)(1/52) = 1/2704

(b) the first card is a heart and the second card is the '6' of

hearts.

P (first card is a heart)  =  1/4

P (second card is the '6' of hearts) = 1/52

P (first card is a heart and the second card is the '6'

of hearts):

=   (1/4) (1/52)  =  1/208



Probability of independent events