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

961. An urn contains 3 white and 4 red balls. 3 balls are drawn one by one with replacement. Find the probability distribution of the number of red balls.

78 Views

962. Find the probability distribution of green balls drawn when 3 balls are drawn one by one without replacement from a bag containing 3 green and 5 white balls.

90 Views

963. Find the probability distribution of white balls drawn when 3 balls are drawn one by one without replacement from a bag containing 4 white and 6 red balls.

71 Views

964. A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If the random variable X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.

152 Views

Long Answer Type

965. Two bad eggs are mixed accidentally with 10 good one. Find the probability distribution of the number of bad eggs in 3, drawn at random, from this lot.

128 Views

966. From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

There are 30 bulbs which include 6 defective bulbs.
Probability of getting a defective bulb =

6 over 30 space equals 1 fifth

Probability of getting a good bulbs =

1 minus 1 fifth space equals space 4 over 5

Let X be random variable of defective bulbs in a sample of 4 bulbs.
X can take the values 0, 1, 2, 3, 4.

therefore space space space space space space space space space space space straight P left parenthesis straight X space equals space 0 right parenthesis space equals space open parentheses 4 over 5 close parentheses to the power of 4 space equals space 256 over 625

straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight C presuperscript 4 subscript 1 space open parentheses 4 over 5 close parentheses cubed space open parentheses 1 fifth close parentheses space equals space 4 space cross times space 64 over 125 space cross times space 1 fifth space equals space 256 over 625 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight C presuperscript 4 subscript 2 space open parentheses 4 over 5 close parentheses squared space open parentheses 1 fifth close parentheses squared space equals space 6 cross times 16 over 25 cross times 1 over 25 space equals 96 over 625 straight P left parenthesis straight X space equals space 3 right parenthesis space equals space straight C presuperscript 4 subscript 3 space open parentheses 4 over 5 close parentheses space open parentheses 1 fifth close parentheses cubed space equals space 4 cross times 4 over 5 cross times 1 over 125 space equals 16 over 625 straight P left parenthesis straight X space equals space 4 right parenthesis space equals space open parentheses 1 fifth close parentheses to the power of 4 space equals space 1 over 625

∴ probability distribution of defective bulbs is

150 Views

967. Find the probability distribution of number of doublets in three throws of a pair of dice.

134 Views

968. A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

113 Views

969. Three cards are drawn successively with replacement from a well-shuffled deck of 52 cards. A random variable X denotes the number of spades in three cards. Determine the probability distribution of X.

84 Views

Short Answer Type

970. Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as:
number greater than 4

72 Views