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Probability

Short Answer Type

391. A die is rolled. If an even number shows up, another die is rolled. But if an odd number shows up, a coin is tossed. Write the sample space of the experiment.

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392. A coin is tossed. If it results in a head, a die is thrown. If the die shows up an even number, the coin is tossed again. Write the sample space of the experiment.

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393. There are 3 red and 3 black balls in a box. A die is rolled and if it shows an even number, a ball is drawn from the box. Write the sample space S.

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394. There are two apples (A) and four oranges (O) in a box. A coin is tossed and if it is a head, one fruit is drawn from the box. Write die sample space S for the experiment.

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395. Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and is classified as defective (D) or non-defective (N). Write the sample space of this experiment.

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396. A die is rolled. If it shows 1 or 2, a coin is tossed. Write the sample space for the experiment

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Long Answer Type

397. A die is thrown. Describe the following events:

(i) A : a number less than 7.

(ii) B : a number greater than 7.

(iii) C : an multiple of 3.

(iv) D : a number less-than 4.

(v) E : an even number greater than 4.

(vi) F : a number is not less than 3.

Also, find, A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A - C, D - E, F', E ∩ F'

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Short Answer Type

398. A die is rolled. Let E be the event “die shows 4” and F be the event “die shows an even number”. Are E and F multually exclusive?

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Long Answer Type

399. Three coins are tossed once. Let A denote the event ‘three heads show’, B denote the event “two heads and one tail show”, C denote the event ‘three tails show and D denote event ‘a head shows on the first coin’, which events are: (i) multually exclusive? (ii) simple? (iii) compound?

Three coins are tossed. The sample space is:
 $left curly bracket stack HHH comma with underbrace below space stack HHT comma space HTH comma space THH comma with underbrace below space stack TTH comma space THT comma space HTT comma with underbrace below TTT with underbrace below right curly bracket$
Event A: three heads show.
$rightwards double arrow$ A = {HHH}
Event B: two heads and one tail shows.
$rightwards double arrow$ B = {HHT, HTH, THH}
Event C: three tails show.
$rightwards double arrow$ C= {TTT}
Event D: a head shows on the first coin.
$rightwards double arrow$ D = {HHH, HHT, HTH, HTT}

(i) $straight A intersection straight B space equals space left curly bracket HHH right curly bracket space intersection space left curly bracket HHT comma space THH comma space HTH right curly bracket space equals left curly bracket space right curly bracket equals space straight ϕ$
∴ A and B are mutually exclusive.
 $straight A intersection straight C space equals space left curly bracket HHH right curly bracket space intersection space left curly bracket TTT right curly bracket space equals space straight ϕ$
∴ A and C are mutually exclusive.
 $straight A intersection straight D space equals space left curly bracket HHH right curly bracket space intersection space left curly bracket HHH comma space HHT comma space HTH comma space HTT right curly bracket space equals space left curly bracket HHH right curly bracket space not equal to space straight ϕ$
∴ A and D are not mutally exclusive
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∴ B and C are mutually exclusive.
 $straight B intersection straight D space equals space left curly bracket HHT comma space HTH comma space THH right curly bracket space intersection space left curly bracket HHH comma space HHT comma space HTH comma space HTT right curly bracket$
$space space equals left curly bracket HHT comma space HTH right curly bracket space not equal to space straight ϕ$
∴ B and D are not mutually exclusive.
 $space space straight C intersection straight D space equals space left curly bracket TTT right curly bracket space intersection space left curly bracket HHH comma space HHT comma space HTH comma space HTT right curly bracket space equals space straight ϕ$
∴ C and D are mutually exclusive.

(ii) A = {HHH} $rightwards double arrow$ n (A) = 1
∴ A is a simple event.
C = {TTT} $rightwards double arrow$ n(C) = 1
∴ C is a simple event.

(iii) B = {HHT, HTH, THH}
$rightwards double arrow$ n(B) = 3 > 1
∴ B is a compound event.
D = {HHH, HHT, HTH, HTT}
$rightwards double arrow$ n(D) = 4 > 1
∴ D is a compound event.

79 Views

Short Answer Type

400. Three coins are tossed. Describe two events which are mutually exclusive.

120 Views