A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

What is the probability that a randomly chosen two-digit positive integer is multiple of 3?

Five marbles are drawn from a bag which contains 7 blue marbles and 4 black marbles. What is the probability that 3 will be blue and 2 black?

Consider the following experiment of rolling a die.Let A be the event 'getting a prime number' and B be the event'getting an odd number'.Write the sets representing events
A but not B

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

An experiment consists of recording boy-girl composition of families with 2 children
What is the sample space, if we are interested in knowing whether it is a boy or girl in the order of their births?

A and B are two events that P(A) = 0.54, P(B) = 0.69 and \(P(A\cap B)\) = 0.35.
Find (i) P(A ∪ B) (ii) P(A´ ∩ B´) (iii) P(A ∩ B´) (iv) P(B ∩ A´)

The probability that at least one of the events A and B occurs is 0.6. If A and B occurs simultaneously with probability 0.2, then find \(P(\overline { A } )+P(\overline { B } ).\)

Two dice are thrown once. The events A, B, E are as follows
A: Getting an even number on the first die.
B: Getting on the odd number on the first die.
E: Getting the sum of numbers on the dice\(\ge \)10.
Describe the events B^'.

If the odds against the occurrence of an event are 4:7;, find the probability of occurrence of the event.

Four cards are drawn at random from pack of 52 playing cards, Find the probability of getting On card from each suit.

Two unbiased dice are thrown. Find the probability that neither a doublet nor a total of 10 will appear.

One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
an ace

One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
not a black card

Refer to question 6 above, state true or false (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B'
(iv) A and C are mutually exclusive
(v) A and B' are mutually exclusive
(vi) A', B', C are mutually exclusive and exhaustive.

A die is thrown, find the probability of following events:
(i) A prime number will appear.
(ii) A number greater than or equal to 3 will appear.
(iii) A number less than or equal to one will appear.
(iv) A number more than 6 will appear.
(v) A number less than 6 will appear.