Quantitative Reasoning

Probability

Medium

Two dice are thrown simultaneously. What is the probability that 4 will come up on at least one die?

11/36

1/6

7/6

5/18

✅ Correct Option: 1

When two dice are thrown simultaneously, we need to find the probability that at least one die shows a 4.

"At least one" means one 4 or two 4s (i.e., not zero 4s).

When throwing 2 dice:

First die has 6 possible outcomes: 1, 2, 3, 4, 5, 6

Second die has 6 possible outcomes: 1, 2, 3, 4, 5, 6

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

Using the complement method, we find the probability of not getting any 4, then subtract from 1.

For the first die to not show 4:

Possible outcomes: 1, 2, 3, 5, 6 (5 outcomes)

$P(\text{no 4 on first die}) = \dfrac{5}{6}$

For the second die to not show 4:

$P(\text{no 4 on second die}) = \dfrac{5}{6}$

For both dice to not show 4:

$P(\text{no 4 on either die}) = \dfrac{5}{6} \times \dfrac{5}{6}$

$= \dfrac{25}{36}$

$P(\text{at least one 4}) = 1 - P(\text{no 4 on either die})$

$= 1 - \dfrac{25}{36}$

$= \dfrac{36}{36} - \dfrac{25}{36}$

$= \dfrac{11}{36}$

Therefore, the probability that 4 will come up on at least one die is $\dfrac{11}{36}$ .

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If A and B are two disjoint events then

A. A ∩ B = Φ

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Choose the correct answer from the options given below:

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2025: 13 May Shift 1

Suppose we throw a dice once. Then, which one of the following is/are correct?

(A) The probability of getting a number greater than 4 is $\frac{1}{3}$

(B) The probability of getting a number greater than or equal to 4 is $\frac{1}{3}$

(D) The probability of getting a number less than or equal to 6 is 1.

Choose the correct answer from the options given below:

Two dice are thrown simultaneously. What is the probability that 4 will come up on at least one die?

Solution

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