Probability

When a fair die is rolled, the probability of getting a number greater than 4 is:

1. a\(\dfrac{1}{4}\)
2. b\(\dfrac{1}{2}\)
3. c\(\dfrac{1}{3}\)
4. d\(\dfrac{2}{3}\)

A card is drawn at random from a deck of 52 cards. The probability that it is a king is:

1. a\(\dfrac{1}{4}\)
2. b\(\dfrac{1}{13}\)
3. c\(\dfrac{4}{13}\)
4. d\(\dfrac{1}{52}\)

Two coins are tossed simultaneously. The probability of getting at least one head is:

1. a\(1\)
2. b\(\dfrac{1}{2}\)
3. c\(\dfrac{1}{4}\)
4. d\(\dfrac{3}{4}\)

A bag contains 5 red, 4 blue, and 3 green balls. A ball is drawn at random. The probability that it is not red is:

1. a\(\dfrac{1}{3}\)
2. b\(\dfrac{5}{12}\)
3. c\(\dfrac{7}{12}\)
4. d\(\dfrac{3}{4}\)

Two dice are rolled. The probability that the sum equals 7 is:

1. a\(\dfrac{1}{12}\)
2. b\(\dfrac{1}{6}\)
3. c\(\dfrac{5}{36}\)
4. d\(\dfrac{1}{9}\)

From a pack of 52 cards, the probability of drawing a spade or an ace is:

1. a\(\dfrac{1}{13}\)
2. b\(\dfrac{1}{4}\)
3. c\(\dfrac{4}{13}\)
4. d\(\dfrac{17}{52}\)

Cards numbered 1 to 30 are placed in a box; one is drawn at random. The probability that it is a multiple of 3 or 5 is:

1. a\(\dfrac{7}{15}\)
2. b\(\dfrac{1}{2}\)
3. c\(\dfrac{11}{30}\)
4. d\(\dfrac{13}{30}\)

If \(P(A) = 0.4\), then \(P(\text{not } A) =\)

1. a0.4
2. b0.6
3. c0
4. d1

Assertion (A): When a fair die is rolled, the probability of getting an odd number is \(\dfrac{1}{2}\).

Reason (R): \(P(A) = \dfrac{\text{favourable outcomes}}{\text{total outcomes}}\) for equally likely outcomes.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): 15% can be the probability of an event, but \(-1.5\) cannot.

Reason (R): For every event \(E\), \(0 \le P(E) \le 1\).

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): When a coin is tossed once, \(P(\text{head}) = 0.6\).

Reason (R): \(P(\text{not } A) = 1 - P(A)\) for any event \(A\).

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

1. I. The probability of an impossible event is 0.
2. II. The probability of a sure event is 1.
3. III. The sum of probabilities of all elementary events is 1.

Examine the basic probability claims. Which are correct?

1. aOnly I and II
2. bOnly II and III
3. cOnly I and III
4. dAll three

1. I. A standard pack of cards has 52 cards.
2. II. There are 4 aces in a deck of cards.
3. III. There are 12 face cards in a standard deck.

Concerning a standard deck, identify the correct statements:

1. aAll three
2. bOnly II and III
3. cOnly I and III
4. dOnly I and II

1. I. When a fair die is rolled, \(P(\text{getting an even number}) = \dfrac{1}{2}\).
2. II. When two coins are tossed, \(P(\text{both heads}) = \dfrac{1}{4}\).
3. III. When a die is rolled, \(P(\text{getting a number} > 6) = 0\).

Read the dice/coin claims. Which are correct?

1. aOnly I and II
2. bOnly II and III
3. cAll three
4. dOnly I and III

A fair die is thrown once. Match each event in List I with its probability in List II:

1. a(i)-S, (ii)-Q, (iii)-R, (iv)-P
2. b(i)-Q, (ii)-S, (iii)-R, (iv)-P
3. c(i)-Q, (ii)-S, (iii)-P, (iv)-R
4. d(i)-S, (ii)-P, (iii)-R, (iv)-Q

Match each card-event with its probability (52-card deck):

1. a(i)-R, (ii)-S, (iii)-P, (iv)-Q
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-S, (ii)-R, (iii)-Q, (iv)-P
4. d(i)-P, (ii)-Q, (iii)-R, (iv)-S

A box contains 12 balls of which \(x\) are blue. If one ball is drawn at random, the probability of drawing a blue ball is \(\dfrac{x}{12}\). If 6 more blue balls are added, this probability becomes double of the original. Find \(x\).

1. a4
2. b3
3. c6
4. d5

A jar contains 24 marbles, some green and some blue. If a marble is drawn at random and the probability of green is \(\dfrac{2}{3}\), then the number of blue marbles is:

1. a12
2. b16
3. c8
4. d6

Three coins are tossed once. The probability of getting at most 1 head is:

1. a\(\dfrac{1}{8}\)
2. b\(\dfrac{3}{8}\)
3. c\(\dfrac{5}{8}\)
4. d\(\dfrac{1}{2}\)

Two dice are rolled. The probability of getting doublets (same number on both) is:

1. a\(\dfrac{1}{6}\)
2. b\(\dfrac{1}{12}\)
3. c\(\dfrac{5}{36}\)
4. d\(\dfrac{1}{3}\)