S1 Urgent Help Needed

[Freaked out]

hey can somebody solve the o/n 2009 62 Q1

 

[mehranshaikh]

I need some help please.
November 2011, 61, Q7 part 3.

7. Bag A contains 4 balls numbered 2, 4, 5, 8. Bag B contains 5 balls numbered 1, 3, 6, 8, 8. Bag C
contains 7 balls numbered 2, 7, 8, 8, 8, 8, 9. One ball is selected at random from each bag.
(i) Find the probability that exactly two of the selected balls have the same number. [5]
(ii) Given that exactly two of the selected balls have the same number, find the probability that they
are both numbered 2. [2]
(iii) Event X is ‘exactly two of the selected balls have the same number’. Event Y is ‘the ball selected
from bag A has number 2’. Showing your working, determine whether events X and Y are
independent or not.


I can't get how to get the P(X and Y) which is needed for part 3.

 

[mehranshaikh]

hey can somebody solve the o/n 2009 62 Q1

Mean can be seen from the picture being midway between Q1 and Q3. So (63-39)/2 + 39 = Mean

For part 2 63 is at 75%, so from Normal distribution table, .674 covers 75% of area.
Z=X-Mean/S.D
Z= .674
X= 63
Mean= We just calculated.

So just calculate S.D

 

[Freaked out]

for the first part make a probability tree and check out any combination in which there are only two balls with same number .
for the second part just calculate the condition probability with two numbers being two given that they are same.
not sure about the third one

 

[Freaked out]

but I do get is that P(X and Y) means the overall probability that the number from bag A is 2 and two out of three of the balls have the same number.
AS you already have the probability of P(X) which you calculated in the first part and the probability of P(Y) is given which is the probability of the number two ball out of the toatal number of the balls in bag A just simply multiply them. not sure how to prove if they are independent or not.

 

[mehranshaikh]

but I do get is that P(X and Y) means the overall probability that the number from bag A is 2 and two out of three of the balls have the same number.
AS you already have the probability of P(X) which you calculated in the first part and the probability of P(Y) is given which is the probability of the number two ball out of the toatal number of the balls in bag A just simply multiply them. not sure how to prove if they are independent or not.

Thanks!