Algebra

Probability

Medium

core

The probability of simultaneous occurrence of at least one of two events E and F is $p$ . If the probability that exactly one of E, F occurs is $q$ , then $P(\overline{E}) + P(\overline{F})$ is equal to

$q + 2p - 2$

$q - 2p + 2$

$2q - p + 2$

$2q + p - 2$

✅ Correct Option: 2

Let $S=P(E)+P(F)$ and $I=P(E \cap F)$ . Then $S-I=p$ and $S-2I=q$ , so $I=p-q$ and $S=2p-q$ . Hence $P(\overline{E})+P(\overline{F})=2-S=2-2p+q$ .

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: 2 June Shift 1

A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

2022: 23 Aug Shift 1

If answer is correct, the probability that he guesses, is :

2025: 19 May Shift 1

If X is a normal variate with mean 16 and standard deviation 4, then the value of standard normal variate Z corresponding to X = 17 is:

2026: 12 May Shift 2

Given that the events A and B are mutually exclusive such that $P(A)=\dfrac{1}{2}$ , $P(A\cup B)=\dfrac{2}{3}$ and $P(B)=p$ , then the value of $p$ is:

2026: 14 May Shift 2

A pair of coins thrown then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Probability of occurance of head on both coins is	I.	$\dfrac{3}{4}$
B.	Probability of occurance of at least one tail is	II.	$\dfrac{1}{2}$
C.	Probability of occurance of one tail only is	III.	$1$
D.	Probability of a tail appears on one coin given that only one coin shows head.	IV.	$\dfrac{1}{4}$

Choose the correct answer from the options given below:

The probability of simultaneous occurrence of at least one of two events E and F is ppp. If the probability that exactly one of E, F occurs is qqq, then P(E‾)+P(F‾)P(\overline{E}) + P(\overline{F})P(E)+P(F) is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The probability of simultaneous occurrence of at least one of two events E and F is $p$ . If the probability that exactly one of E, F occurs is $q$ , then $P(\overline{E}) + P(\overline{F})$ is equal to