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Mathematics : Probability

Long Answer Type

491.

Two coins are tossed simultaneously. Find the probability of getting:

(i) both tails (ii) no tail (iii) exactly one tail (iv) atmost one tail (v) atleast one tail.

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492. Three coins are tossed simultaneously. Find the probability of (i) exactly 2 heads (ii) all tails (iii) atmost one tail (iv) exactly 1 head (v) atleast 2 tails, (vi) a head on the first toss.

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493. Four coins are tossed simultaneously What is the probability of getting (i) all tails (ii) exactly one tail (iii) exactly 2 heads, (iv) atleast 1 tail (v) atmost 3 heads?

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494. One die is rolled. Find the probability that the number obtained is:
(i) divisible by 2 (ii) not divisible by 2 (iii) an odd number (iv) x such that x ≤ 2 (v) x such that x is a prime number.

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495.

Two dice are rolled simultaneously. Find the probability that:

(i) The sum of numbers on the two dice is less than 9.

(ii) The sum of numbers on the two dice is greater than or equal to 9.

(iii) Even number appears on the first die and a multiple of 3 on the second die.

(iv) Even number appears on the first die and the total of numbers on the two dice is 9.

(v) It is not a doublet.

(vi) The number on the first and second die are (x, y) such that x < 3, y < 4

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496. A die has two faces each with number ‘ 1’, three faces each with number ‘2’ and one face with ‘3’. The die is rolled once, determine
(i) P (2) (ii) P (1 or 3) (iii) P (not 3)

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497. A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be:
(i) red, (ii) yellow, (iii) blue, (iv) not blue, (v) either red or yellow .

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498. A fair coin is tossed 4 times, and a person wins Re 1 for each head and losses Re 1.50 for each tail that turns up. Form the sample space to calculate how many different amounts of money you can have after four tosses and the probability of having each one of those amounts.

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Short Answer Type

499. In a non-leap year, what is the probability of having 52 Tuesdays?

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500. In a leap year, what is the probability of having 53 Fridays?

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