Algebra

Probability

Easy

core

A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

✅ Correct Option: 1

The probability of getting a tail on the coin or a number greater than 3 on the die needs to be determined.

The coin has 2 outcomes: Head (H) or Tail (T)

The die has 6 outcomes: 1, 2, 3, 4, 5, 6

Total combined outcomes = 2 × 6 = 12

The favorable outcomes occur when there is a tail on the coin or a number greater than 3 (that is, 4, 5, or 6) on the die.

When coin shows Tail:

(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) → 6 outcomes

When coin shows Head and die shows a number greater than 3:

(H, 4), (H, 5), (H, 6) → 3 outcomes

Total favorable outcomes = 6 + 3 = 9

The probability is:

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

$\text{Probability} = \dfrac{9}{12}$

$\text{Probability} = \dfrac{3}{4}$

Therefore, the probability that the outcome will be a tail on the coin or a number greater than 3 on the die is $\dfrac{3}{4}$ .

2025: 13 May Shift 1

If the probability of two successes is 9 times the probability of 3 successes in 3 trials of a binomial distribution, then the probability of success in each trial is:

2025: 3 June Shift 1

Which of the following statements are correct?

(A) The mean and variance of the Poisson distribution are equal.

(B) The mean and variance of a Binomial distribution are equal.

(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is $\frac{5}{108}$ .

(D) If the variance of a Poisson distribution is 2, then P(X = 2) = $2e^{-2}$

Choose the correct answer from the options given below:

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) Two events E and F will be independent if $P(E'F')$ is equal to	(I) $1 - P(E/F)$
(B) If $P(F) \neq 0$ , then $P(E'/F)$ is equal to	(II) $P(E) = P(F)$
(C) If E and F are independent events, then	(III) $P(E \cap F') = P(E) \cdot P(F')$
(D) If $P(E \cap F) \neq 0$ and $P(E/F) = P(F/E)$ , then	(IV) $[1-P(E)][1-P(F)]$

Choose the correct answer from the options given below :

2022: 23 Aug Shift 1

Consider an experiment of tossing 3 coins simultaneously. Define the following events:

$E$ = [Three heads or three tails appear]

$F$ = [At least two heads appear] and

$G$ = [At most two heads appear]

Choose the correct option:

2025: 21 May Shift 1

If a random variable y follows Poisson's distribution such that $P(X = 2) = 9 P(X = 4) + 90 P(X = 6)$ , then sum of the mean and variance of X is

2025: 13 May Shift 1

One person speaks truth in 60% of the cases and another person in 80% of the cases. They are likely to agree in stating the same fact in

A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is

Solution

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