11th Std Math Practical
Mathematics and Statistics (Arts and Science)
Answers (Solutions)
Practical No.9
9) Probability
Practical Session No. 9-Probability
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Practical Session No. 9
Probability
(1) The turnout of spectators at the world cup cricket match is dependent upon the weather. On a rainy day the probability of a big turnout is 0.3. If it doesn’t rain, then the probability of big turnout increases by 0.6. The weather forecast gives a probability of 0.75 that it will rain on the day of the match.
Find the probability that (i) there is a big turn out and it rains (ii) there is a big turn out.
(2) A bag contains 7 red and 5 blue balls. A ball is taken at random from the bag, its color is noted and not replaced into the bag. Now a second ball is taken from the bag and its color is noted. Find the probability that one is red and the other is blue.
(3) If 𝑃𝑃(𝐴𝐴)=14 ,𝑃𝑃(𝐵 )=25 𝑎𝑎𝑎𝑎𝑎𝑎𝑡𝑡𝑜𝑜 𝑃𝑃(𝐴𝐴∪𝐵 )=12 then find
1) 𝑃𝑃(𝐴𝐴∩𝐵 ) 2) 𝑃𝑃(𝐴𝐴∩𝐵 ′) 3) 𝑃𝑃(𝐴𝐴′∩𝐵 ) 4) 𝑃𝑃(𝐴𝐴′∪𝐵 ′) 5) 𝑃𝑃(𝐴𝐴′∩𝐵 ′)
(4) 2% of the population have a certain blood disease in a serious form. 10% have it in a mild form and 88% don’t have it at all. A new blood test is developed, the probability of testing positive is 9/10 if the subject has the serious form, 6/10 if the subject has the mild form, and 1/10 if the subject doesn’t have the disease. A subject is tested positive. What is the probability that the subject has serious form of the disease?
(5) A coin is tossed until a head appears or until it has been tossed three times. Given that head does not occur on the first toss, what is the probability that coin is tossed three times ?
(6) From a group of 8 boys and 5 girls, a committee of 5 is to be formed. Find the probability that a committee contains i) 3 boys and 2 girls ii) at least 3 boys.
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