Page 77 - Math SL HB Sem 3

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L [Maximum mark: 14] tv!"9 \z rz-

Bag A contains three white balls and four red balls Two balls are chosen at random
without replacement.

(a) (, Copy and complete the following tree diagram. (Do notwrite on this page.)

2
Whire
6

White
7
Red

White
4
1 Red

Red

(ii) Find the probability that two white balls are chosen.
[5 marksJ

Bag B contains four white balls and three red balls. when two balls are chosen at
random without replacement from bag B, the probability that rhey are both white is 2
'7 .

A standard die is rolled. If I or 2 is obtained, two balls are chosen without replacement
from bag A, otherwise they are chosen from bag B.

(b) Find the probabiliry that the rwo balls are white.
[5 marksJ

(c) Given that both balls are white, find the probability that they were chosen from
bagA.
[4 marksJ

M I 2/5/MATME/SP I /ENG/TZ2IXX

J . [Maximum mark: 8J

p
The random variable X has the following probability distribution, with (X > l)
= 0.5 .
,r 0 l 2 3
P(x =x) p q 0.2

(a) Find the value of r.
[2 marksJ

(b) Given that E(X)
=1.4 , find the value of p and of q . [6 marks]
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