Chapter 13
Probability
Every example and exercise of the chapter, worked in full. Each page gives the question, the complete solution, the reason behind every step, and the basics it rests on.
New to this chapter? Start with the quick lesson: the formulas, the question types and how to crack each one →Examples
- Example 1 when and worked
- Example 2Two children: both boys, given at least one is a boyworked
- Example 3Card numbered 1 to 10: even, given it is more than 3worked
- Example 4School of 1000 students: Class XII, given a girlworked
- Example 5Die thrown three times: 4 on the third, given 6 then 5worked
- Example 6Two dice with sum 6: a 4 appears at least onceworked
- Example 7Coin, then coin or die: die above 4, given at least one tailworked
- Example 8Urn: two black balls drawn without replacementworked
- Example 9Three cards: two kings, then an aceworked
- Example 10Die: are 'multiple of 3' and 'even' independent?worked
- Example 11Die thrown twice: odd on the first and odd on the secondworked
- Example 12Three coins: which of the pairs of E, F, G are independentworked
- Example 13If E and F are independent, so are E and worked
- Example 14Independent A, B: at least one is worked
- Example 15Construction job on time: total probability over a strike, worked
- Example 16Red ball drawn: was it from Bag II? worked
- Example 17Three boxes of coins: the other coin is also gold, worked
- Example 18HIV test: has HIV, given a positive report, worked
- Example 19Defective bolt: made by machine B, worked
- Example 20Doctor arrives late: did he come by train? worked
- Example 21Speaks the truth 3 times in 4: reports a six, worked
- Example 22Four boxes of coloured balls: black ball from box III, worked
- Example 23A and B throw a die in turn until a 6: and worked
- Example 24Machine set-up: correct, given 2 acceptable items, worked
Exercise 13.1
- Exercise 13.1 · Q1 and from three given probabilitiesworked
- Exercise 13.1 · Q2 from and worked
- Exercise 13.1 · Q3, , from worked
- Exercise 13.1 · Q4 when worked
- Exercise 13.1 · Q5Intersection and conditionals from worked
- Exercise 13.1 · Q6Coin tossed three times: in three casesworked
- Exercise 13.1 · Q7Two coins tossed once: in two casesworked
- Exercise 13.1 · Q8Die thrown three times: 4 on the third, given 6 then 5worked
- Exercise 13.1 · Q9Family picture: son on an end, given father in the middleworked
- Exercise 13.1 · Q10Black and red dice: sum above 9 given black 5; sum 8 given red below 4worked
- Exercise 13.1 · Q11Die with , , : six conditional probabilitiesworked
- Exercise 13.1 · Q12Two children: both girls, given the youngest or at least one is a girlworked
- Exercise 13.1 · Q13Question bank: easy, given multiple choiceworked
- Exercise 13.1 · Q14Two dice showing different numbers: sum 4worked
- Exercise 13.1 · Q15Die, then die or coin: a tail, given at least one die shows 3worked
- Exercise 13.1 · Q16 (MCQ) when , worked
- Exercise 13.1 · Q17 (MCQ)Events with worked
Exercise 13.2
- Exercise 13.2 · Q1 for independent A and Bworked
- Exercise 13.2 · Q2Two cards without replacement: both blackworked
- Exercise 13.2 · Q3Box of oranges approved: three good ones drawnworked
- Exercise 13.2 · Q4Coin and die: are 'head' and '3' independent?worked
- Exercise 13.2 · Q5Die with red and green numbers: are 'even' and 'red' independent?worked
- Exercise 13.2 · Q6Are E and F independent when ?worked
- Exercise 13.2 · Q7Find p: mutually exclusive, then independentworked
- Exercise 13.2 · Q8Independent A and B: four probabilitiesworked
- Exercise 13.2 · Q9worked
- Exercise 13.2 · Q10Independent? Given worked
- Exercise 13.2 · Q11Independent A and B: and, and not, or, neitherworked
- Exercise 13.2 · Q12Die tossed thrice: an odd number at least onceworked
- Exercise 13.2 · Q13Two balls drawn with replacement: red and blackworked
- Exercise 13.2 · Q14A and B solve a problem independentlyworked
- Exercise 13.2 · Q15One card: in which cases are E and F independent?worked
- Exercise 13.2 · Q16Hostel newspapers: neither, and two conditionalsworked
- Exercise 13.2 · Q17 (MCQ)Even prime number on each of a pair of diceworked
- Exercise 13.2 · Q18 (MCQ)A condition for A and B to be independentworked
Exercise 13.3
- Exercise 13.3 · Q1Urn topped up with the colour drawn: second ball red, worked
- Exercise 13.3 · Q2Two bags: the red ball came from the first bag, worked
- Exercise 13.3 · Q3Hostel or day scholar: the A-grade student lives in the hostel, worked
- Exercise 13.3 · Q4Knows or guesses: knew the answer, given it is correct, worked
- Exercise 13.3 · Q5Blood test: has the disease, given a positive result, worked
- Exercise 13.3 · Q6Three coins: the two-headed coin, given heads, worked
- Exercise 13.3 · Q7Insured drivers: a scooter driver, given an accident, worked
- Exercise 13.3 · Q8Two machines: defective item made by B, worked
- Exercise 13.3 · Q9Board election: new product introduced by the second group, worked
- Exercise 13.3 · Q10Die, then coin: threw 1 to 4, given exactly one head, worked
- Exercise 13.3 · Q11Three operators: defective item produced by A, worked
- Exercise 13.3 · Q12Lost card is a diamond, given two diamonds are drawn, worked
- Exercise 13.3 · Q13 (MCQ)Speaks the truth with : head actually appeared, worked
- Exercise 13.3 · Q14 (MCQ): , option (C)worked
Miscellaneous Exercise
- Miscellaneous · Q1 if , and if worked
- Miscellaneous · Q2Two children: both males given at least one male, ; both females given the elder is female, worked
- Miscellaneous · Q3Grey hair: the person selected is male, worked
- Miscellaneous · Q4At most 6 of 10 people right-handed, worked
- Miscellaneous · Q5A leap year with 53 Tuesdays, worked
- Miscellaneous · Q6Four boxes of marbles: a red marble came from box A, B or C, worked
- Miscellaneous · Q7Heart attack: the patient followed meditation and yoga, worked
- Miscellaneous · Q8A determinant of 0s and 1s is positive, worked
- Miscellaneous · Q9Two subsystems: A fails given B failed (0.5), and A fails alone (0.05)worked
- Miscellaneous · Q10Ball moved between bags: the moved ball was black, worked
- Miscellaneous · Q11 (MCQ) gives , option (A)worked
- Miscellaneous · Q12 (MCQ) gives , option (C)worked
- Miscellaneous · Q13 (MCQ) gives , option (B)worked
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