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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?

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Short Answer Type

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

Three coins are tossed.
$rightwards double arrow$ The sample space is: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Event E: three heads show
$rightwards double arrow$ E = {HHH}
Event F: three tails show
$rightwards double arrow$ F = {TTT}
$straight E intersection straight F space equals space left curly bracket HHH right curly bracket space intersection space left curly bracket TTT right curly bracket space equals space straight ϕ$
Hence, E and F are mutually exclusive event.

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