Quantitative Reasoning Probability Test 3 Online

1. Three groups A,B,C are contesting for a position on the Board of directors of a company. The probabilities of their winning are 0.5, 0.3,0.2 respectively. If the group a wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is?

2. There are 6 positive and 8 negative numbers. Four numbers are chosen at random and multiplied. The probability that the product is a positive number is?

3. A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is probability that the balls drawn contain no blue ball?

4. A committee consists of 9 experts taken from three institutions A,B and C, of which 2 are from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is?

5. Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number?

6. One hundred identical coins each with probability p as showing up heads are tossed. If 0<p<1 and the probability of heads showing on 50 coins is equal to that of heads on 51 coins,  then the value of p is?

7. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1,2 are 0.45,0.05 and 0.50 respectively. As summing that outcomes are independent, the probability of India getting at least 7 points is?

8. In a defective 6 faced die with numbers 1 to 6 inscribed, the probability of getting an odd number is twice the probability of getting an even number. Find the probability of getting a 2 digit prime number on adding 2 successive throws of the die.

9. A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?

10. A man bets on number 16 on a roulette wheel 14 times and loses each time. On the 15th spin, he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and therefore unable to decide whether to bet on 16 or 12 in the 15th spin. Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36).

11. Out of 20 consecutive positive integers, two are chosen at random. The probability that their sum is odd is?

12. The probability that a student is not a swimmer is 1/5. Then the probability that out of the five students, four are swimmers, is?