Algebra

Probability

Hard

core

A letter is known to have come either from LONDON or CLIFTON. On the envelope, just two consecutive letters 'ON' are visible then the probability that the letter has come from CLIFTON is:

$\dfrac{5}{17}$

$\dfrac{9}{17}$

$\dfrac{8}{17}$

$\dfrac{12}{17}$

✅ Correct Option: 1

LONDON has 5 consecutive pairs, of which 2 are ON, so $P(ON|L) = \dfrac{2}{5}$ .

CLIFTON has 6 consecutive pairs, of which 1 is ON, so $P(ON|C) = \dfrac{1}{6}$ .

By Bayes' theorem, $P(C|ON) = \dfrac{\frac12\cdot\frac16}{\frac12\cdot\frac25+\frac12\cdot\frac16} = \dfrac{5}{17}$ .

2025: 14 May Shift 2

A lot of 50 watches is known to have 10 defective watches. If 8 watches are selected one by one with a replacement at random, then the probability that there will be at least one defective watch is:

2025: 15 May Shift 2

If A speaks truth in 75% cases and B speaks truth in 80% cases, then the probability that they contradict each other in a statement, is:

2026: 21 May Shift 2

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then

Match the LIST-I with LIST-II

LIST-I		LIST-II
A. $P(X=0)$		I. 1
B. $P(X=1)$		II. $\dfrac{19}{34}$
C. $P(X=2)$		III. $\dfrac{13}{34}$
D. $P(X<3)$		IV. $\dfrac{1}{17}$

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

The value of $k$ is

2022: 30 Aug Shift 1

Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

2026: 14 May Shift 2

A bag contains 5 white, 4 black and 3 red balls. Which of the following statements are True?

A. The probability of drawing three red balls one by one without replacement is $\frac{1}{220}$

B. One by one three balls drawn without replacement then probability that third ball is red is $\frac{1}{4}$

C. The probability of drawing 2 white balls one by one without replacement is $\frac{3}{4}$

D. One by one 3 balls are drawn without replacement then probability that third ball is red is $\frac{3}{4}$

Choose the correct answer from the options given below:

A letter is known to have come either from LONDON or CLIFTON. On the envelope, just two consecutive letters 'ON' are visible then the probability that the letter has come from CLIFTON is:

Solution

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