1) A school offers japanese and arabic as two foreign languages. the probabilitiy that a student who studies japanese also studies arabic is 1/4 and 1/5 of the students who study arabic also studies japanese too. among the students, 1/5 of them do not study any of the two languages . what is the probability that a student in the school studies both languages? Are the events of studying japanese and arabic independent? ( answer provided 1/10,not independent) explain pls
2)Bag A contains 3 red balls and 2 green balls whereas bag B contain 2 red balls and 3 green balls. two balls r withdrwan from bag a to be put into bag b . then two balls are taken out from B to be put in bag A. what is the probability that bag A now contains 3 red balls and 2 green balls.? answer 10/21
2R => Bag B has 4R and 3G. Probability = (3/5)(2/4) = 6/20. Bag A has 1R, 2G.
1R, 1G => Bag B has 3R and 4G. Probability = 2 (3/5)(2/4) = 12/20. Bag A has 2R, 1G.
2G => Bag B has 2R and 5G. Probability = (2/5)(1/4) = 2/20. Bag A has 3R.
Now consider each of the possible bag B's:
4R, 3G: The two balls taken need to be 2R for Bag A to have 3R and 2G. The probability of this is (4/7)(3/6) = 12/42.
3R, 4G: The two balls taken need to be 1R 1G for Bag A to have 3R and 2G. The probability of this is 2 (3/7)(4/6) = 24/42.
2R 5G: The two balls taken need to be 2G for Bag A to have 3R and 2G. The probability of this is (5/7)(4/6) = 20/42.
So the total probability is (6/20)(12/42) + (12/20)(24/42) + (2/20)(20/42) = .......