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The correct choice is (b) 16

To elaborate: Each BULB can have two CASES i.e. either defective or non-defective. Then TOTAL number of OUTCOMES will be 2^4 = 16.

Correct CHOICE is (a) event

The explanation: Any SUBSET of SAMPLE space is known as event. Event means occurrence of some particular OUTCOMES.

The CORRECT OPTION is (B) Φ

To explain I would say: Impossible event has no outcome in favour. So, it is denoted by empty SET Φ.

The correct option is (d) 1/18

For EXPLANATION: If TWO dice are simultaneously rolled then total number of possible OUTCOMES is 6*6 =36.

We can get 11 as sum in these cases {(5,6), (6,5)}. So, probability of getting sum 11 is 2/36 = 1/18.

The correct choice is (b) 1/16

To EXPLAIN: Each bulb can have two cases i.e. either defective or non-defective. Then total NUMBER of outcomes will be 2^4 = 16.

So, the PROBABILITY that all the BULBS are defective is 1/16.

The correct choice is (a) S-A

Best EXPLANATION: If the EVENT is A then COMPLEMENTARY event is not A.

Not A MEANS S-A. So, complementary event of event A is represented by A’ = S-A.

Correct option is (b) 1/2

For explanation: There are SIX POSSIBLE OUTCOMES on dice i.e. 1 to 6.

Even NUMBERS on dice are 2,4,6 i.e. three outcomes in favour of the event.

So, probability of getting an even number on dice is 3/6 = 1/2.

Correct choice is (a) SIMPLE EVENT

The EXPLANATION: If an event has only one sample POINT then it is called simple event.

e.g. All heads on tossing n coins.

Correct ANSWER is (a) True

Explanation: Yes, for every EVENT there EXIST some COMPLEMENTARY event. If the event is A then complementary event is not A.

Right answer is (B) 15/16

To explain I WOULD say: Each BULB can have two cases i.e. either defective or non-defective. Then total number of outcomes will be 2^4 = 16.

Probability that all the bulbs are defective is 1/16.

So, the probability that at LEAST one bulb is non-defective is 1-1/16 = 15/16.

The correct choice is (d) 3/4

Easy explanation: If two coins are tossed SIMULTANEOUSLY TOTAL number of possible OUTCOMES are 4.

{HH, TT, HT, TH} out of which {HH, HT, TH} favour the event.

So, probability of getting at least ONE head = 3/4.

Correct CHOICE is (b) {}

The EXPLANATION is: A = {(1,1), (1,2), (2,1)}

B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

“A and not B” contains ELEMENTS which are in A but not in B.

So, A and not B = {}.

Right answer is (a) 1/2

To ELABORATE: If two COINS are TOSSED simultaneously total number of possible outcomes are 4.

{HH, TT, HT, TH} out of which {HT, TH} favour the event.

So, probability of getting exactly ONE tail = 2/4 = 1/2.

The correct choice is (b) False

For explanation I would say: If A∪B=S then SET is SAID to be mutually exhaustive. If both SETS A and B have together form SAMPLE space then it is a pair of mutually exhaustive sets.

Correct option is (d) 2

The BEST I can explain: Since probability is ratio of NUMBER of outcomes in favour to the total number of possible outcomes. And number of outcomes in favour are ALWAYS less than or equal to total number of possible outcomes. So, probability is always less than or equal to 1.

Right answer is (c) 1/4

The BEST I can explain: If TWO coins are tossed simultaneously total number of possible outcomes are 4.

{HH, TT, HT, TH} out of which {HH} favour the event.

So, probability of GETTING all heads = 1/4.

The correct choice is (a) 0

Explanation: IMPOSSIBLE event has no outcome in favour. And probability is ratio of NUMBER of OUTCOMES in favour to the total number of possible outcomes. So, probability of impossible event is zero.

Correct answer is (c) 1/4

The BEST I can explain: If two coins are tossed simultaneously TOTAL number of possible outcomes are 4.

{HH, TT, HT, TH} out of which {TT} favour the event.

So, PROBABILITY of getting no heads = 1/4.

Right answer is (b) 0

Explanation: There are six POSSIBLE outcomes on DICE i.e. 1 to 6.

7 does not appear on a dice so PROBABILITY of getting 7 on a dice is ZERO.

Right option is (d) B but not A

Explanation: Event “B but not A” contains ELEMENTS which are PRESENT in B but not in A.

It is represented by B-A or B∩A’.

Right option is (B) False

To elaborate: If two coins are tossed simultaneously then S = {HH, HT, TH, TT}.

“Exactly one head APPEARS” includes HT, TH. It has more than one sample point so it is compound EVENT not SIMPLE event.

Right option is (B) 1

Explanation: Sure EVENT has all OUTCOMES in FAVOUR i.e. number of outcomes in favour equal to the total number of possible outcomes.

And PROBABILITY is ratio of number of outcomes in favour to the total number of possible outcomes.

So, probability of sure event will be 1.

Right CHOICE is (C) 1/3

For explanation I would SAY: There are six possible outcomes on dice i.e. 1 to 6.

Composite NUMBERS on dice are 4,6 i.e. two outcomes in favour of the event.

So, probability of getting a composite number on dice is 2/6 = 1/3.

The CORRECT answer is (C) A∩B’

The explanation: Event “A but not B” contains ELEMENTS which are present in A but not in B.

It is REPRESENTED by A-B or A∩B’.

Correct choice is (a) A∪B

The best explanation: Event “A or B” CONTAINS ELEMENTS which are either in A or in B or in both. It is also called union of the two sets and is REPRESENTED by A∪B.

The CORRECT choice is (a) 0

Explanation: Since number greater than 6 cannot APPEAR on dice so probability of getting a number greater than 6 is zero.

The CORRECT answer is (a) 1/2

For explanation: There are six possible outcomes on dice i.e. 1 to 6.

Prime numbers on dice are 2,3,5 i.e. THREE outcomes in favour of the event.

So, probability of getting a prime NUMBER on dice is 3/6 = 1/2.

The CORRECT choice is (a) {(1,1), (1,2), (2,1)}

Best explanation: A = {(1,1), (1,2), (2,1)}

B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

“A and B” contains ELEMENTS PRESENT in both A and B.

So, A and B = {(1,1), (1,2), (2,1)}.

Right option is (b) 12

Explanation: If head come on coin then RED DICE can have 6 outcomes so total 1*6 = 6 outcomes.And if TAIL come on coin then blue dice can have 6 outcomes so total 1*6 = 6 outcomes.

So, total number of possible outcomes = 6 + 6 = 12.

The correct ANSWER is (c) A but not B

Easy EXPLANATION: Event “A but not B” contains ELEMENTS which are PRESENT in A but not in B.

It is REPRESENTED by A-B or A∩B’.

Correct choice is (c) SAMPLE space

To EXPLAIN I would say: Set which contains all possible outcomes is called sample space. It can also be called UNIVERSAL set.

The correct answer is (d) A’∩B

For explanation: Event “B but not A” contains elements which are PRESENT in B but not in A.

It is REPRESENTED by B-A or B∩A’.

The correct OPTION is (d) None head appears

The explanation is: We KNOW complementary of at LEAST ONE is none. So, complementary event for “At least one head appears” is none head appears.

Right option is (B) A∩B

Best explanation: EVENT “A and B” contains elements which are both in A and B. It is also called intersection of two sets and is REPRESENTED by A∩B.

The correct answer is (a) A or B

For EXPLANATION I WOULD say: Event “A or B” CONTAINS elements which are either in A or in B or in both. It is also called union of the two sets.

The correct answer is (B) False

The best EXPLANATION: Since probability is the ratio of number of OUTCOMES in favour to TOTAL number of possible outcomes and number (counting) cannot be NEGATIVE so, probability cannot be negative.

Correct OPTION is (c) 2^n

The best explanation: If n coins are TOSSED simultaneously total number of POSSIBLE outcomes are 2^n.

For 2 coins, it is 4. For 3 coins it is 8 etc.

Right ANSWER is (d) 1/2

Easiest explanation: An UNBIASED coin can have HEAD or tail as outcome i.e. there are TWO possible outcomes.

So, probability of getting tail on an unbiased coin is 1/2.

The correct ANSWER is (c) {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

The BEST explanation: A = {(1,1), (1,2), (2,1)}

B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

“A or B” CONTAINS elements of either A or B or both.

So, A or B = {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}.

The correct choice is (d) 3/4

Easiest explanation: If two coins are TOSSED SIMULTANEOUSLY total NUMBER of possible outcomes are 4.

{HH, TT, HT, TH} out of which {HT, TH, TT} favour the event.

So, probability of getting at most ONE head = 3/4.

Correct choice is (c) Ratio of number of outcomes in FAVOUR to TOTAL number of outcomes

The BEST I can explain: Probability is chance of an OUTCOME to APPEAR. It is the ratio of number of outcomes in favour to total number of outcomes.

Correct ANSWER is (d) {(1,3), (2,2), (3,1)}

The EXPLANATION is: A = {(1,1), (1,2), (2,1)}

B= {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

“B and not A” CONTAINS elements which are in B but not in A.

So, B and not A = {(1,3), (2,2), (3,1)}.

Correct choice is (b) 4

Easiest EXPLANATION: If two coins are tossed simultaneously total NUMBER of possible OUTCOMES are 4.

{HH, TT, HT, TH}

The CORRECT answer is (a) 1/2

To elaborate: If two coins are TOSSED simultaneously total NUMBER of possible outcomes are 4.

{HH, TT, HT, TH} out of which {HT, TH} FAVOUR the event.

So, probability of getting exactly one head = 2/4 = 1/2.

Right option is (b) False

The EXPLANATION is: If A∩B=ϕ then set is said to be mutually EXCLUSIVE not mutually exhaustive. If both sets A and B have no element in COMMON then it is a pair of mutually exclusive sets.