NCERT Solutions for Class 12 Science Maths Chapter 7 – Probability
Here are the NCERT solutions for Class 12 Science Maths Chapter 7 on Probability, featuring clear step-by-step explanations. Widely favored by Class 12 Science students, these solutions prove valuable for efficiently completing homework assignments and exam preparation. You can access all questions and answers from Chapter 7 of the NCERT Book for Class 12 Science Maths here at no cost. Page No 538: Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E). ANSWER: It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2 Page No 538: Question 2: Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32 ANSWER: It is given that P(B) = 0.5 and P(A ∩ B) = 0.32 Page No 538: Question 3: If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find (i) P(A ∩ B) (ii) P(A|B) (iii) P(A ∪ B) ANSWER: It is given that P(A) = 0.8, P(B) = 0.5, and P(B|A) = 0.4 (i) P (B|A) = 0.4 (ii) (iii) P(A∪B) = P(A) + P(B) − P(A∩B)⇒P(A∪B)=0.8 + 0.5 − 0.32 = 0.98PA∪B = PA + PB – PA∩B⇒PA∪B=0.8 + 0.5 – 0.32 = 0.98 Page No 538: Question 4: Evaluate P (A ∪ B), if 2P (A) = P (B) =and P(A|B) = ANSWER: It is given that, It is known that, Page No 538: Question 5: If P(A), P(B) =and P(A ∪ B) =, find (i) P(A ∩ B) (ii) P(A|B) (iii) P(B|A) ANSWER: It is given that (i) (ii) It is known that, (iii) It is known that, Page No 538: Question 6: A coin is tossed three times, where (i) E: head on third toss, F: heads on first two tosses (ii) E: at least two heads, F: at most two heads (iii) E: at most two tails, F: at least one tail ANSWER: If a coin is tossed three times, then the sample space S is S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} It can be seen that the sample space has 8 elements. (i) E = {HHH, HTH, THH, TTH} F = {HHH, HHT} E ∩ F = {HHH} (ii) E = {HHH, HHT, HTH, THH} F = {HHT, HTH, HTT, THH, THT, TTH, TTT} E ∩ F = {HHT, HTH, THH} Clearly, (iii) E = {HHH, HHT, HTT, HTH, THH, THT, TTH} F = {HHT, HTT, HTH, THH, THT, TTH, TTT} Page No 539: Question 7: Two coins are tossed once, where (i) E: tail appears on one coin, F: one coin shows head (ii) E: not tail appears, F: no head appears ANSWER: If two coins are tossed once, then the sample space S is (ii) E = {HH} F = {TT} ∴ E ∩ F = Φ P (F) = 1 and P (E ∩ F) = 0 ∴ P(E|F) = Page No 539: Question 8: A die is thrown three times, E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses ANSWER: If a die is thrown three times, then the number of elements in the sample space will be 6 × 6 × 6 = 216 Page No 539: Question 9: Mother, father and son line up at random for a family picture E: son on one end, F: father in middle ANSWER: If mother (M), father (F), and son (S) line up for the family picture, then the sample space will be S = {MFS, MSF, FMS, FSM, SMF, SFM} ⇒ E = {MFS, FMS, SMF, SFM} F = {MFS, SFM} ∴ E ∩ F = {MFS, SFM} Page No 539: Question 10: A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. ANSWER: Let the first observation be from the black die and second from the red die. When two dice (one black and another red) are rolled, the sample space S has 6 × 6 = 36 number of elements. A: Obtaining a sum greater than 9 = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} B: Black die results in a 5. = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)} ∴ A ∩ B = {(5, 5), (5, 6)} The conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5, is given by P (A|B). P(A|B) = P(A∩B)P(B) = 236636 = 26 = 13PA|B = PA∩BPB = 236636 = 26 = 13 (b) E: Sum of the observations is 8. = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)} F: Red die resulted in a number less than 4. The conditional probability of obtaining the sum equal to 8, given that the red die resulted in a number less than 4, is given by P (E|F). Page No 539: Question 11: A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find (i) P (E|F) and P (F|E) (ii) P (E|G) and P (G|E) (ii) P ((E ∪ F)|G) and P ((E ∩ G)|G) ANSWER: When a fair die is rolled, the sample space S will be S = {1, 2, 3, 4, 5, 6} It is given that E = {1, 3, 5}, F = {2, 3}, and G = {2, 3, 4, 5} (i) E ∩ F = {3} (ii) E ∩ G = {3, 5} (iii) E ∪ F = {1, 2, 3, 5} (E ∪ F) ∩ G = {1, 2, 3, 5} ∩{2, 3, 4, 5} = {2, 3, 5} E ∩ F = {3} (E ∩ F) ∩ G = {3}∩{2, 3, 4, 5} = {3} Page No 539: Question 12: Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional …
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