Algebra

Probability

Medium

core

A die is thrown three times. If the first throw is a five, the probability of getting 14 as the sum is

$\frac{1}{9}$

$\frac{1}{18}$

$\frac{1}{36}$

$\frac{1}{54}$

✅ Correct Option: 1

A die is thrown three times, and the first throw is already 5.

The total sum needed is 14. Since the first throw is 5, the sum needed from the 2nd and 3rd throws is:

$14 - 5 = 9$

When throwing a die twice, each die can show 1, 2, 3, 4, 5, or 6.

Total possible outcomes $= 6 \times 6 = 36$

Finding the outcomes where the 2nd and 3rd throws sum to 9:

2nd throw = 3, 3rd throw = 6 → sum = 9

2nd throw = 4, 3rd throw = 5 → sum = 9

2nd throw = 5, 3rd throw = 4 → sum = 9

2nd throw = 6, 3rd throw = 3 → sum = 9

Favorable outcomes = 4

The probability is:

$\text{Probability} = \dfrac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$

$\text{Probability} = \dfrac{4}{36}$

$\text{Probability} = \dfrac{1}{9}$

Therefore, the probability of getting a sum of 14 is $\dfrac{1}{9}$ .

2025: 13 May Shift 1

A random variable X has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	k²	2k²	7k² + k

The value of $P(4 < x < 7)$ is equal to

2023: 22 May Shift 3

The probability that a student is not a swimmer is $\frac{1}{5}$ . Then the probability that out of five students, four are swimmers is :

2026: 18 May Shift 2

An alphabet has been selected from English alphabets. What is the probability that it is a vowel given that it precedes 'M' ?

2026: 30 May Shift 1

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ . If all the three students try to solve the problem independently, the probability that the problem is solved, is:

2025: 22 May Shift 1

If E and F are independent events associated with an experiment, then which one of the following statements is correct?

2025: 3 June Shift 2

The probability distribution of a random variable X is

X	0	1	2	3	4
P(X)	0.2	k	k	2k	k

Match List-I with List-II

List-I	List-II
(A) value of k	(I) $\frac{16}{25}$
(B) $P(x \geq 2)$	(II) $\frac{9}{25}$
(C) $P(x = 3)$	(III) $\frac{4}{25}$
(D) $P(x < 2)$	(IV) $\frac{8}{25}$

Choose the correct answer from the options given below:

A die is thrown three times. If the first throw is a five, the probability of getting 14 as the sum is

Solution

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