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