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#### Introduction To Probability Theory Three Marks Questions

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. An integer is chosen at random from the first ten positive integers. Find the probability that it is
(i) an even number (ii) multiple of three

2. A die is rolled. If it shows an odd number, then find the probability of getting 5.

3. Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

4. If A and B are two events associated with a random experiment for which
P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15.
Find (i) P(only B)
(ii) P(B)
(iii) P(only A)

5. A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event 'second die shows 5’. Find $P(A\cup B)$ .

6. Two unbiased die are thrown. Find the probability that the sum is 8 or greater if 3 appears on the first die.

7. One card is drawn from a well shuffled pack of 52 cards. If E is the event, "the card drawn is a king or queen" and F is the event "the card drawn is a queen or an ace", then find P(E/F).

8. The probability that a person will get an electric contract  $\frac { 2 }{ 3 }$ and the probability that he will not get plumbing contract is $\frac { 4 }{ 7 }$. If the probability of getting atleast one contract is $\frac { 2 }{ 3 }$. What is the probability tht he will get both?

9. A fair dice is rolled. Consider the following events A = {1, 3, 5}, B = {2, 3} and C ={2, 3, 4, 5} Find (i) P(A/B) and P(B/A) (ii) P(A$\cap$B/C)

10. A and B are two events such that P(A) $\neq$ 0. Find P(B/A) if (i) A is a subset of B (ii) A$\cap$B = $\phi$