Plus Two Maths Chapter Wise Previous Questions Chapter 13 Probability are part of Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 13 Probability.

## Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 13 Probability

Question 1.

a. The probability distribution of a random variable is given by P(x). What is ΣP(x)?

b. The following is a probability distribution function of a random variable.

i. Find k

ii. Find P(x>3)

iii. Find p(-3<x<4)

iv. Find P(x>-3) **[March-2018]
**Answer:

a. The probability distribution of a random variable is given by p(x).

then P(x) = 1 then ΣP(x) = 1

ie, sum of all the probabilities in a probability distribution must be one.

b. i. k+2k+3k+4k+5k+7k+8k+9k+10k +11k+12k = 1

72k=1, k=

ii. p(x>3) =P(x=4) + P(x = 5)

iii. P(-3 < x < 4) = P(x = -2) + P(x= -1) + P(x= 0 ) + P(x = 1) + P(x=2) + P( x = 3)

Question 2.

a. If A and B are two events such that A ⊂B and P(A) ≠0 then P(A/B) is

a.

b.

c.

d.

b. There are two identical bags. Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 4 black balls. One ball is drawn at random from one of the bags.

i. Find the probability that the ball drawn is red.

ii. If the ball drawn is red what is the probability that it was drawn from hag I?

**OR
**Consider the following probability distribution of a random variable X.

i. Find the value of K.

ii. Determine the Mean and variance of X.

**[March-2017]**

Answer:

**a.**

Since A ⊂B, ∴ P(A ∩B) = P(A)

b . i. Let ∈

_{1}be the event of choosing the bag I, ∈

_{2}be the event of choosing the bag II and A be the event of drawing a red ball.

Then P(∈

_{1}) = P(∈

_{2}) =

Question 3.

If P(A) = 0.3, P(B) =0.4, then the value of P(A∪B) where A and B are independent events is

(i) 0.48

(ii) 0.51

(iii) 0.52

(iv) 0.58

b. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be diamonds. Find the probability of the lost card being a diamond.

**OR
**A pair of dice is thrown 4 times. If getting a doublet is considered as a success.

1. find the probability of getting a doublet.

2. Hence, find the probability of two successes.

**[March-2016]**

Answer:

Question 4.

The probability distribution of a random variable X taking values 1, 2, 3, 4, 5 is given

a. Find the value of P

b. Find the mean of X

c. Find the variance of X **[March- 2015]
**Answer:

Question 5.

a. For two independent events A and B, which of the following pair of events need not be independent?

i. A’ , B’

ii. A , B’

iii. A’ , B

iv. A – B, B-A

b. If P (A) = 0.6, P(B) = 0.7 and p(A∪B)=0.9,then find and ** [March-2015]
**Answer:

Question 6.

A and B try to solve a problem independently. The probability that A solves the problem is 1/2 and that B solves the problem is 1/3. Find the probability that

a. Both of them solve the problem.

b. The problem is solved.

**OR
**If A and B are two independent events then,

a. Prove that A and B’ are independent events.

b. Show that the probability of occurrence of atleast one of A and B is 1-P(A’) P(B’).

Answer:

Question 7.

a. If A and B are independent event, prove that A’ and B’ are independent events.

b. A box contains 30 defective and 30 non- defective bulbs. Two bulbs are drawn at random the events A & B are defined as follows:

A: The first bulb is defective

B: The second bulb is non-defective Find P(A) and P(B). Prove that A and B are independent events.

Answer:

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