Fill in the blanks in following table: (ii) $P(A) = 0.35, P(B) = ..., P(A \cap B) = 0.25, P(A \cup B) = 0.6$

A card is selected from a pack of 52 cards. (a) How many points are there in the sample space?

Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5.

state true or false: (give reason for your answer) (iv) A and C are mutually exclusive

If E and F are events such that $P(E) = \frac{1}{4}$, $P(F) = \frac{1}{2}$ and $P(E \text{ and } F) = \frac{1}{8}$, find (i) $P(E \text{ or } F)$,

Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5.

state true or false: (give reason for your answer) (v) $A$ and $B'$ are mutually exclusive.

Fill in the blanks in following table: (iii) $P(A) = 0.5, P(B) = 0.35, P(A \cap B) = ..., P(A \cup B) = 0.7$

A die is thrown. Describe the following events: (ii) B: a number greater than 7

A and B are events such that $P(A) = 0.42, P(B) = 0.48$ and $P(A \text{ and } B) = 0.16$. Determine (ii) $P(\text{not } B)$ and

A card is selected from a pack of 52 cards. (b) Calculate the probability that the card is an ace of spades.

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is (ii) 12

Three coins are tossed once. Find the probability of getting (viii) no tail

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8, B: 2 occurs on either die
C: the sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?

Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined (i) $P(A) = 0.5, P(B) = 0.7, P(A \cap B) = 0.6$

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that (ii) The student has opted neither NCC nor NSS.

A coin is tossed twice, what is the probability that atleast one tail occurs?

Three coins are tossed once. Find the probability of getting (vii) exactly two tails

Three coins are tossed. Describe (v) Three events which are mutually exclusive but not exhaustive.

A and B are events such that $P(A) = 0.42, P(B) = 0.48$ and $P(A \text{ and } B) = 0.16$. Determine (i) $P(\text{not } A)$,

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?

A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is (ii) a consonant