LEVEL-11. The probability that it will rain tomorrow is 0.85. What is

1.	LEVEL-11. The probability that it will rain tomorrow is 0.85. What is the probability that it will norain tomorrow?2. A die is thrown. Find the probability of getting:(i) a prime number [NCERT, CBSE 2019] (ii) 2 or 4(iii) a multiple of 2 or 3(iv) an even prime number [CBSE 2008(v) a number greater than 5[CBSE 2008] (vi) a number lying between 2 and 6(vii) a composite number [CBSE 2019][NCERT, CBSE 20193. Three coins are tossed together. Find the probability of getting:(i) exactly two heads(ii) at most two heads(ii) at least one head and one tail. (iv) no tails4. A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher numbe5. Two unbiased dice are thrown. Find the probability that the total of the numbers on thdice is greater than 10.[CBSE 20186. A card is drawn at random from a pack of 52 cards. Find the probability that the cardrawn is(i) a black king(ii) either a black card or a king
Answer» Solution 1 :- <P> The probability that it will be rain tomorrow is 0.85 . As we know that, P( E ) + P( not E ) = 1 Here, P ( E ) = 0.85 So, 1 - 0.85 = 0.15 Hence, The probability that it will be no rain tomorrow is 0.15 Solution 2 :- ( 1 )Total outcomes of die = 1 , 2 , 3 , 4 , 5 , 6 = 6 Favourable outcomes = 2 , 3 , 5 = 3 THEREFORE, Probability = Favourable outcomes/Total outcomes P( getting prime numbers ) = 3/6 = 1/2 ( 2 ) Total outcomes of die = 6 Favourable outcomes = 2 or 4 = 1 P( getting 2 ) = 1/6 P( getting 4) = 1/6 (3) Multiple of 2 = 4 , 6 or 3 = 6 Total outcomes = 6 Favourable outcome = 2 or 1 Now, P( getting multiple of 2) = 2/6 = 1/3 P( getting multiple of 3) = 1/6 4) Total outcomes = 6 Favourable outcomes = 2 , 4 , 6 P( getting even numbers) = 3/6 = 1/2 5) Total outcomes = 6 Favourable outcome = 1 ( only 6 is greater than 5) P ( getting greater than 5) = 1 / 6 6) Total outcomes = 6 Favourable outcome = 3,4,5 = 3 P( getting numbers between 2 and 6 ) = 3/6 = 1/2 7) Total outcomes = 6 Favourable outcomes = 4 , 6 P( getting composite number) = 2/6 = 1/3 Solution 3 :- Three COINS are tossed together, Total outcomes = 8 [ HHH, HTH, HHT, THH, HHT, THT, TTH , TTT ] 1) Exactly two heads Total outcomes = 8 Favourable outcome = 3 P ( getting exactly 2 head) = 3/8 2) At most two heads Total outcomes = 8 Favourable outcome = 4 P( getting At most 2 heads) = 4/8 = 1/2 3) Total outcomes = 8 Favourable outcome = 6 P( getting one head and one tail) = 6/8 4) Total Outcomes = 8 Favourable outcome = 1 P( getting no tails) = 1/8 Solution 4 :- Total outcomes = 36 Favourable outcomes, = 9 Therefore, P( chance of throwing B) = 9/36 = 1/4 Solution 5 :- Total outcomes = 36 Favourable outcome = 3 ( (5,6), ( 6 ,5) , ( 6 ,6 ) ) P( getting greater than 10) = 3/36 = 12 Solution 6 :- 1) Total outcomes = 52 Total black king = 2 Favourable outcome = 2 P ( getting black king) = 2/52 = 1/26 2) Total outcomes = 52 Total black cards or black king = 28 Favourable outcome = 28 P( getting EITHER black card or king) = 28/52 = 7/13 $.$

LEVEL-11. The probability that it will rain tomorrow is 0.85. What is the probability that it will norain tomorrow?2. A die is thrown. Find the probability of getting:(i) a prime number [NCERT, CBSE 2019] (ii) 2 or 4(iii) a multiple of 2 or 3(iv) an even prime number [CBSE 2008(v) a number greater than 5[CBSE 2008] (vi) a number lying between 2 and 6(vii) a composite number [CBSE 2019][NCERT, CBSE 20193. Three coins are tossed together. Find the probability of getting:(i) exactly two heads(ii) at most two heads(ii) at least one head and one tail. (iv) no tails4. A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher numbe5. Two unbiased dice are thrown. Find the probability that the total of the numbers on thdice is greater than 10.[CBSE 20186. A card is drawn at random from a pack of 52 cards. Find the probability that the cardrawn is(i) a black king(ii) either a black card or a king

Answer»

Solution 1 :-

<P>

The probability that it will be rain tomorrow is 0.85 .

As we know that,

P( E ) + P( not E ) = 1

Here, P ( E ) = 0.85

So,

1 - 0.85 = 0.15

Hence, The probability that it will be no rain tomorrow is 0.15

Solution 2 :-

( 1 )Total outcomes of die = 1 , 2 , 3 , 4 , 5 , 6 = 6

Favourable outcomes = 2 , 3 , 5 = 3

THEREFORE,

Probability = Favourable outcomes/Total outcomes

P( getting prime numbers ) = 3/6 = 1/2

( 2 ) Total outcomes of die = 6

Favourable outcomes = 2 or 4 = 1

P( getting 2 ) = 1/6

P( getting 4) = 1/6

(3) Multiple of 2 = 4 , 6 or 3 = 6

Total outcomes = 6

Favourable outcome = 2 or 1

Now,

P( getting multiple of 2) = 2/6 = 1/3

P( getting multiple of 3) = 1/6

4) Total outcomes = 6

Favourable outcomes = 2 , 4 , 6

P( getting even numbers) = 3/6 = 1/2

5) Total outcomes = 6

Favourable outcome = 1 ( only 6 is greater than 5)

P ( getting greater than 5) = 1 / 6

6) Total outcomes = 6

Favourable outcome = 3,4,5 = 3

P( getting numbers between 2 and 6 ) = 3/6 = 1/2

7) Total outcomes = 6

Favourable outcomes = 4 , 6

P( getting composite number) = 2/6 = 1/3

Solution 3 :-

Three COINS are tossed together,

Total outcomes = 8 [ HHH, HTH, HHT, THH, HHT, THT, TTH , TTT ]

1) Exactly two heads

Total outcomes = 8

Favourable outcome = 3

P ( getting exactly 2 head) = 3/8

2) At most two heads

Total outcomes = 8

Favourable outcome = 4

P( getting At most 2 heads) = 4/8 = 1/2

3) Total outcomes = 8

Favourable outcome = 6

P( getting one head and one tail) = 6/8

4) Total Outcomes = 8

Favourable outcome = 1

P( getting no tails) = 1/8

Solution 4 :-

Total outcomes = 36

Favourable outcomes, = 9

Therefore,

P( chance of throwing B) = 9/36 = 1/4

Solution 5 :-

Total outcomes = 36

Favourable outcome = 3 ( (5,6), ( 6 ,5) , ( 6 ,6 ) )

P( getting greater than 10) = 3/36 = 12

Solution 6 :-

1) Total outcomes = 52

Total black king = 2

Favourable outcome = 2

P ( getting black king) = 2/52 = 1/26

2) Total outcomes = 52

Total black cards or black king = 28

Favourable outcome = 28

P( getting EITHER black card or king)

= 28/52 = 7/13 $.$