Algebra Test No. 9

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A coin is tossed. Find the probability that neither head nor tail turns up. A coin is tossed three times. Find the probability that i. Exactly one tail turns up. ii. At least two tails turns up. iii. No tail turns up. 3. A die is thrown. Find the probability that i. An odd number comes up. ii. A perfect square comes up. 4. A multiple of 7 comes up. Two coins are tossed. Find the probability that i. At least one head turns up. ii. No head turns up. 5. Two dice are thrown. Find the probability that i. The sum of the numbers on the dice is at least 11. ii. The sum of the numbers on the dice is divisible by 9. iii. The number on the upper face of the first die is greater than the number on the upper face of the second die. iv. The sum of the numbers on their upper faces is a perfect square. 6. There are 15 tickets bearing number from one to fifteen in a bag and one ticket is drawn at random from the bag. Find the probability of the event that the ticket drawn i. Bears an even number. ii. Bears a number which is a multiple of 5. 7. What is the probability of two – digit of number formed from the digits 2,3,5,7,9 if repetition of digits is not allowed? Also find the probability of the event that the two – digit number is a multiple of five. 8. A coin is tossed thrice. Find the probability of the events that i. Head appears twice. ii. Head appears at the most twice. 9. A die is thrown. Find the probability of the events that i. the number divisible by three comes up. ii. The number on the upper face is greater than two. 10. Two dice are thrown. Find the probability of the events. i. The product of the numbers on their upper faces is twelve. ii. The numbers on their upper faces is same. iii. The sum of the number on their upper faces is a multiple of 5. 11. Find the probability that a leap year selected at random will have 53 Sundays. 12. Three boys A, B and C are in a race. A is twice as likely to win as B and B is twice as likely to win as C and P(A) + P(B) + P(C) = 1. What are the respective probabilities of winning?