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

971. Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as:
six appears on at least one die

74 Views

972. Find the mean μ, variance σ² for the following probability distribution:

92 Views

973. Find the mean μ, variance σ² for the following probability distribution:

91 Views

Long Answer Type

974. Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

99 Views

975. Find the mean number of heads in three tosses of a fair coin.

107 Views

976. Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Since 1 cannot be greater than the other selected number.
∴ X can take values 2, 3, 4, 5, 6.
∴ P(X = 2) = P(2 and a number less than 2 are selected)
= P(1 and 2 are selected)
$Syntax error from line 1 column 349 to line 1 column 452. Unexpected '<mlongdiv '.$
P(X = 3) = P(3 and a number less than 3 are selected)
$equals space fraction numerator 2 over denominator straight C presuperscript 6 subscript 2 end fraction space equals 2 over 15$
[∵ (1, 3) and (2, 3) can be selected]
P(X = 4) = P(4 and a number less than 4 are selected)
$equals space fraction numerator 3 over denominator straight C presuperscript 6 subscript 2 end fraction space equals space 3 over 15$
[∵ (1, 4), (2, 4) and (3, 4) can be selected]
P(X = 5) = P(5 and a number less than 5 are selected)
$equals space fraction numerator 4 over denominator straight C presuperscript 6 subscript 2 end fraction space equals 4 over 15.$
[∵ (1, 5), (2, 5), (3, 5) and (4, 5) can be selected]
P(X = 6) = P(6 and a number less than 6 are selected)
$equals space fraction numerator 5 over denominator straight C presuperscript 6 subscript 2 end fraction space equals space 5 over 15$
[∵ (1, 6), (2, 6), (3, 6), (4, 6) and (5, 6) can be selected]
∴ probability distribution table is

$therefore$ Expectation of X = E(X) = $sum from blank to blank of cross times space straight P left parenthesis straight X right parenthesis$

$equals space 2 cross times 1 over 15 plus 2 space cross times space 2 over 15 plus 4 space cross times 3 over 15 plus 5 space cross times 4 over 15 plus 6 space cross times space 5 over 15 equals space fraction numerator 2 plus 6 plus 12 plus 20 plus 30 over denominator 15 end fraction space equals 70 over 15 space equals 14 over 3.$

100 Views

977. Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

89 Views

978. Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

920 Views

979. Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

79 Views

980. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19, 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X ? Find mean, variance and standard deviation of X.

93 Views