Page 85 - Math SL HB Sem 3

I l. Two fair 4-sided dice, one red and one green, are thrown. For each die, the faces are labelled l.
2. i,4. The score for each die is the number which lands face down.

(a) List the pairs ofscores thal give a sum of6.
(J)

The probability distribution for the sum ofthe scores on the two dice is shown below.

Sunr .+ 5 6 7 8
l 4 3 I
Probabilitv
l6 l6 l6 l6

(b) Find the value ofp, ofq, and ofr.
(3)

Fred plays a game. He throws two fair 4-sided dice four times. He wins a prize ifthe sum is 5
on three or more throws.

(c) Find the probability that Fred wins a prize.
(6)
(Total l2 marks)

12. Two boxes contain numbered cards as shown below.

J .t 5 I l0 l0

Two cards are drawn at random, one from each box.

(a) Copy and complete the table below to show all nine equally likely outcomes.

j,9
3. t0

3. t0
\21

Let be the sum ofthe numbers on the two cards.
^t
(b) Wrile down all the possible values ofS.
(2)

(c) Find the probability ofeach value ofS.
(2)

(d) Find rhe e\pected \alue ol S.
(3)

(e) Anna plays a game where she wins $50 ifS is even and loses S30 ifS is odd.
Anna plays the game 36 times. Find the amount she expects to have at the end ofthe 36
games.
(3)
(Total l2 marks)

([