Algebra

Probability

Easy

applied

Two dice are thrown simultaneously. If X denotes the number of sixes, then the mean of X is :

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{3}{4}$

$\frac{1}{3}$

✅ Correct Option: 4

X counts sixes in two independent throws, so X is binomial with $n=2$ and $p=\frac{1}{6}$ .

Hence the mean is $np=2\cdot\frac{1}{6}=\frac{1}{3}$ .

2022: 23 Aug Shift 1

If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is :

2026: 15 May Shift 1

Let A and B are two events associated to a random experiment, then

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $P(A \cap B) + P(A \cap \overline{B})$	I. $P(A \cup B)$
B. $P(A \cap B) + P(\overline{A} \cap B)$	II. $P(A) + P(B)$
C. $P(A \cap B) + P(\overline{A} \cap B) + P(A \cap \overline{B})$	III. $P(A)$
D. $P(A \cup B) + P(A \cap B)$	IV. $P(B)$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

Three bad eggs are mixed with 7 good ones. If two eggs are drawn one by one without replacement, then the probability distribution of the number (X) of bad eggs drawn is:

X	0	1	2
P(X)	1/4	1/2	1/4

X	0	1	2
P(X)	15/61	20/61	26/61

X	0	1	2
P(X)	7/15	7/15	1/15

X	0	1	2
P(X)	1/8	1/4	5/8

2025: 21 May Shift 1

A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is

2025: 13 May Shift 1

If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is

2025: 30 May Shift 1

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

Two dice are thrown simultaneously. If X denotes the number of sixes, then the mean of X is :

Solution

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