Aarav, who lived on Earth, went to Mars and met Jadoo, Badoo, Kadoo and Ladoo there. All four of them, who were residents of Mars, had some chocolates with them. On the arrival of Aarav, they became so happy that all of them gave away all their chocolates to Aarav. The number of chocolates with Jadoo, Badoo, Kadoo and Ladoo were 15, 40, k01 and 122 respectively as per the number system prevalent on their planet. They also told Aarav that the number of chocolates they had was in an arithmetic progression in the number system used on their planet. Aarav was an expert in number systems. If Aarav counted the chocolates that he received, which of the following cannot represent the number of chocolates that he counted? 1)122 2)233 3)442 4)278 5)None of these
let say in mars the base is 6.
15=11 base 10
40=24 base 10
122=50 base 10
4th number will be 37 (for arithmetic progression)
Hence, sum=11+24+37+50=112
Now, 122 in base 10 in base 7 = 233 122 in base 10 in base 5 = 442
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
5.A and B play 12 games of chess. A wins 6, B wins 4 and two are drawn. They agree to play 3 more games. Find the probability that: (i) A wins all 3 games (ii) Two games end in a tie (iii) A and B win alternately (iv) B wins at least 1 game. (v) A wins at least 1 game.
Three unbiased dice I, II and III are rolled simultaneously. Assuming that the sum of the numbers on the dice is 15, what is the probability that the die I has shown a 4?
4. A question is given to three students A, B and C whose chances of solving it are ˝, 1/3, ź respectively. What is the probability that the problem will be solved?
Aarav, who lived on Earth, went to Mars and met Jadoo, Badoo, Kadoo and Ladoo there. All four of them, who were residents of Mars, had some chocolates with them. On the arrival of Aarav, they became so happy that all of them gave away all their chocolates to Aarav. The number of chocolates with Jadoo, Badoo, Kadoo and Ladoo were 15, 40, k01 and 122 respectively as per the number system prevalent on their planet. They also told Aarav that the number of chocolates they had was in an arithmetic progression in the number system used on their planet. Aarav was an expert in number systems. If Aarav counted the chocolates that he received, which of the following cannot represent the number of chocolates that he counted? 1)122 2)233 3)442 4)278 5)None of these
Deja vu Three unbiased dice I, II and III are rolled simultaneously. Assuming that the sum of the numbers on the dice is 15, what is the probability that the die I has shown a 4?
Deja vu Three unbiased dice I, II and III are rolled simultaneously. Assuming that the sum of the numbers on the dice is 15, what is the probability that the die I has shown a 4?
Deja vu Three unbiased dice I, II and III are rolled simultaneously. Assuming that the sum of the numbers on the dice is 15, what is the probability that the die I has shown a 4?
5.A and B play 12 games of chess. A wins 6, B wins 4 and two are drawn. They agree to play 3 more games. Find the probability that:(i) A wins all 3 games(ii) Two games end in a tie(iii) A and B win alternately(iv) B wins at least 1 game.(v) A wins at least 1 game.
i) (1/2)(1/2)(1/2) = 1/8
ii) C(3, 2)*{(2/12)(2/12)(1/2 + 1/3)} = 5/72
iii) (1/2)(1/3)(1/2) + (1/3)(1/2)(1/3) = 5/36
iv) 1 - (2/3)(2/3)(2/3) = 19/27 {2/3 is the probability that B doesn't win}
6.The odds against A solving a problem are 7:5 and the odds in favour of B solving it are 12:9. What is the probability that if both of them solve it, it will be solved.
5.A and B play 12 games of chess. A wins 6, B wins 4 and two are drawn. They agree to play 3 more games. Find the probability that:(i) A wins all 3 games(ii) Two games end in a tie(iii) A and B win alternately(iv) B wins at least 1 game.(v) A wins at least 1 game.
6.The odds against A solving a problem are 7:5 and the odds in favour of B solving it are 12:9. What is the probability that if both of them solve it, it will be solved.