| Class XII |
Mathematics |
Mathematics Part-II |
7 |
F) = P({THH}) = Now,supposewearegiventhatthefirstcoinshowstail,i.e.Foccurs,thenwhatis the probability of occurrence of E? With the information of o... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
P(S|F) = P(F|F) = 1 We know that P(S∩F) P(F) P(S|F) = = =1 P(F) P(F) P(F∩F) P(F) Also P(F|F) = P(F) = P(F) =1 Thus P(S|F) = P(F|F) = 1 Property 2 I... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
given that B has already occurred. Solution The sample space has 216 outcomes. (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) .. (2,6,4) Now A =... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
Fig 13.1 described as S = {(H,H), (H,T), (T,1), (T,2), (T,3), (T,4), (T (T,6)} where (H, H) denotes that both the tosses result into headand(T,i)de... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
E : head on third tossF : heads on first two tosses (ii) E : at least two headF : at most two heads (iii) E : at most two t,ilsF : at least one tai... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
of the Exercises 16 and 17 choose the correct answer: 16. If P(A) = 2 , P(B) = 0, then P(A|B) is (A) 0 (B) 2 (C) notdefined (D) 1 Reprint 2026-27 P... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
P(K|K) P(A|KK) = 4 × 3 × 4 = 2 52 51 50 5525 13.4 IndependentEvents Consider the experiment of drawing a card from a deck of 52 playing cards, in w... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
Definition 3 Let E and F be two events associated with the same random experiment, then E and F are said to be independent if P(E ∩ F) = P(E) . P (... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
and E ∩ F = {6} 2 1 3 1 1 Then P(E) = 6 3, P(F)= 6 2 and P(E∩ F)= 6 Clearly P(E ∩ F) = P(E). P (F) Hence E and F are independent events. Example 11... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
P (F) . P(G) Hence, the events (E and F) are independent, and the events (E and G) and (F and G) are dependent. Example 13 Prove that if E and F ar... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
of the hypothesis E. i Bayes'theoremisalsocalledtheformulafortheprobabilityof"causes".Sincethe E'i are a partition of the sample space S, one and o... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be appr... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
12. Adieistossedthrice.Findtheprobabilityofgettinganoddnumberatleastonce. 13. Twoballsaredrawnatrandomwithreplacementfromaboxcontaining10black and8... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags.We can find th... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
is a partition of the sample space S. It may be mentioned that the partition of a sample space is not unique. There can be several partitions of th... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
1,2,..., ni Reprint 2026-27 PROBABILITY 425 Therefore, P (A) = P (E )1P (A|E )1+ P (E ) 2 (A|E ) 2 ... + P (E )PnA|E ) n n or P(A) = ∑ P(E jP(A|E )... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
Thus, the probability that a person selected at random is actually having HIV given that he/she is tested HIV+ive is 0.083. Example19Inafactorywhic... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
probability that he comes by train? Solution Let E be the event that the doctor visits the patient late1an2 l3t 4 , T , T , T betheevents thatthedo... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
not speak the truth 4 4 Thus, by Bayes' theorem, we get P(S1|E) = Probability that the report of the man that six has occurred is actually a six P(... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination.At the end o... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
1% produced by machine B were defective.All the items are put into one stockpile and then one item is chosen at randomfromthisandisfoundtobedefecti... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
PROBABILITY 433 (A) 4 (B) 1 (C) (D) 2 5 2 5 5 14. If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the followingiscorrect? P(B... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
the game. Find their respective probabilities of winning, ifAstarts first. Solution Let S denote the success (getting a ‘6’) and F denote the failu... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
)1+ P(B ) 2(A|B ) 2 0.8×0.9×0.9 648 = = =0.95 0.8×0.9×0.9 +0.2×0.4×0.4 680 Miscellaneous Exercise on Chapter 13 1. A and B are two events such that... |
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| Class XII |
Mathematics |
Mathematics Part-II |
7 |
the patient followed a course of meditationandyoga? 8. If each element of a second order determinant is either zero or one, what is the probability... |
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