Let x denotes the number of heads in a simultaneous toss of three coins, then P(0 < x ≤ 3) Option 1: 1/2 Option 2: 3/4 Option 3: 7/8 Option 4: 1

Answer: 7/8. Solution: When tossing 3 coins simultaneously, let x denote the number of heads obtained. The condition 0 When tossing 3 coins, each coin shows either H (Head) or T (Tail). Total possible outcomes = 2 x 2 x 2 = 8 All possible outcomes:, Outcome, Number of Heads (x), HHH, 3, HHT, 2, HTH, 2, HTT, 1, THH, 2, THT, 1, TTH, 1, TTT, 0, Outcomes where 0 P(0 < x ≤ 3) = (Favorable outcomes)/(Total outcomes) P(0 < x ≤ 3) = 7/8 Therefore, the probability is 7/8.

Algebra

Probability

Medium

common

Let x denotes the number of heads in a simultaneous toss of three coins, then $P(0 < x \leq 3)$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{7}{8}$

✅ Correct Option: 3

When tossing 3 coins simultaneously, let $x$ denote the number of heads obtained.

The condition $0 < x \leq 3$ means $x$ can be 1, 2, or 3 (at least one head).

When tossing 3 coins, each coin shows either H (Head) or T (Tail).

Total possible outcomes $= 2 \times 2 \times 2 = 8$

All possible outcomes:

Outcome	Number of Heads (x)
HHH	3
HHT	2
HTH	2
HTT	1
THH	2
THT	1
TTH	1
TTT	0

Outcomes where $0 < x \leq 3$ (i.e., $x = 1, 2,$ or $3$ ):

$x = 1$ : HTT, THT, TTH → 3 outcomes

$x = 2$ : HHT, HTH, THH → 3 outcomes

$x = 3$ : HHH → 1 outcome

Favorable outcomes $= 3 + 3 + 1 = 7$

Alternatively, only TTT has 0 heads, so favorable outcomes $= 8 - 1 = 7$

$P(0 < x \leq 3) = \dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$P(0 < x \leq 3) = \dfrac{7}{8}$

Therefore, the probability is $\dfrac{7}{8}$ .

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:

2025: 14 May Shift 2

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

2025: 3 June Shift 2

Let X denotes the number of heads in a simultaneous toss of three coins, then $P(0 < X < 3)$ is

2023: 30 May Shift 3

The mean number of heads in two tosses of a coin is :

2026: 29 May Shift 1

If A and B are event such that $P(A)=\dfrac{1}{2}$ , $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. The probability distribution of number of aces is given by:

Let x denotes the number of heads in a simultaneous toss of three coins, then P(0<x≤3)P(0 < x \leq 3)P(0<x≤3)

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Let x denotes the number of heads in a simultaneous toss of three coins, then $P(0 < x \leq 3)$