Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Probability

Short Answer Type

981. In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).

88 Views

Long Answer Type

982. Find the variance of the number obtained on a throw of an unbiased die.

128 Views

983. A die is tossed twice. Getting a number greater than 4 is considered a success. Find the variance of the probability distribution of the number of successes.

215 Views

984. Two bad eggs are mixed accidentally with 10 good ones. Three eggs are drawn at random without replacement from this lot. Find the mean and variance for the number of bad eggs.

400 Views

985. Three bad eggs got mixed up with 7 good eggs. If three eggs are drawn (without replacement) from 10 eggs, find the mean and variance for the number of bad eggs among them.

Number of good eggs = 7
Number of bad eggs = 3
∴ total number of eggs = 7 + 3 = 10
Let X denote the random variable ‘bad egg is obtained’. X takes the values 0, 1, 2, 3.
$straight P left parenthesis straight X space equals space 0 right parenthesis space equals space 7 over 10 cross times 6 over 9 cross times 5 over 8 space equals 210 over 720 straight P left parenthesis straight X space equals space 1 right parenthesis space equals space 3 over 10 cross times 7 over 9 cross times 6 over 8 plus 7 over 10 cross times 3 over 9 cross times 6 over 8 plus 7 over 10 cross times 6 over 9 cross times 3 over 8 space equals 126 over 720 plus 126 over 720 plus 126 over 720 space equals space 378 over 720 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space 3 over 10 cross times 2 over 9 cross times 7 over 8 plus 3 over 10 cross times 7 over 9 cross times 2 over 8 plus 7 over 10 cross times 3 over 9 cross times 2 over 8 space equals 42 over 720 plus 42 over 720 plus 42 over 720 space equals 126 over 720 straight P left parenthesis straight X space equals space 3 right parenthesis space equals space 3 over 10 cross times 2 over 9 cross times 1 over 8 space equals 6 over 720$
$therefore$ X takes the values 0, 1, 2, 3 with probabilities $210 over 720 comma space 378 over 720 comma space 126 over 720 comma space 6 over 720$

$straight mu space equals space sum from blank to blank of straight x space straight p subscript straight i space equals space 648 over 720 space equals space 9 over 10 straight sigma squared space equals space sum from blank to blank of straight x squared space straight p subscript straight i space minus space straight mu squared space equals space 936 over 720 minus 81 over 720 space equals space 13 over 10 minus 81 over 100 space equals space fraction numerator 130 minus 81 over denominator 100 end fraction space equals space 49 over 100 therefore space space space space space mean space equals space straight mu space equals space 9 over 10 comma space space variance space equals space 49 over 100$

237 Views

986. Five defective bulbs are accidentally mixed with twenty good ones. It is not possible to just look at a bulb and tell whether or not a bulb is defective. Four bulbs are drawn at random from this lot. Find the mean number of defective bulbs drawn.

835 Views

987. Two cards are drawn simultaneously (or successively, without replacement) from a well-shuffled deck of 52 cards. Compute σ² for the number of aces.

82 Views

988. In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

138 Views