Question

1)A card is drawn at random from a well shuffled pack of 52 playing cards. Find
the probability that the drawn card is :
1) Neither a red card nor a queen ii) A card of spade or an ace iii) A number
card or a king. iv) a red card and a face card v) an ace and a black honour
card
2) Two dies are thrown simultaneously. What is the probability that
(i) Sum of the two numbers appearing on the top is less than or equal to 10?
(ii) 5 will not come on either of them iii) 5 will come up on at least one?
iv)5 will come up on both dice
3) A dice has 6 faces marked 0,1,1,1,4,4. What is the probability of getting;
i) 4
ii)
iii) 0 iv) 1 or 0 v) 4 and 1
4) Find the value of tan? 10º – cot? 80°
(2015)
tan 15°sin 25°
5) Evaluate
(2016)
cot 75° +
15° cos 65°
6) Prove that -cos A
COS A
'1-sin A
+
'
cOS A
1+sin A
cos A. = 2sec A
(2015)
7) If m = cos @ – sin 0 and n = cos 0 + sin 0 then show that
Vm
(2016) 22
V
v1- tan ²0
(2012)​

Answer 1

Answer:

Step-by-step explanation:

1(a) neither a red nor a queen

favorable outcome=52-26-2

                               =52-28

                               =24

so probability of getting neither red nor queen is 24/52

                                                                                  =6/13

(b) a card of spade or an ace

favorable outcome=16

probability of getting spade or ace=16/52

                                                          =4/13  

(c) a number card or king

favorable outcome=40

so probability of getting a number card or king=40/52

                                                                              =10/13

(d)a red card and a face card

favorable outcome=6

probability of  getting a red card and a face card is 6/52

                                                                                     =3/26

(e)an ace and a black honor card

favorable outcome=7

probability of getting an ace and a black honor card=7/52

2(1)

favorable outcome 1,1  1,2 1,,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3 3,4 3,5 3,6 3,7 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 6,1 6,2 6,3 6,4

=34

probability of getting less than or equal to 10 is 34/36

=17/18

2(2)

favorable outcome=1,1 1,2 1,3 1,4 1,6 2,1 2,2 2,3 2,4 2,6 3,1 3,2 3,3 3,4 3,6 4,1 4,2 4,3 4,4 4,6 6,1 6,2 6,3 6,4 6,6

probability of getting no fives=25/36

2(3)

favorable outcome= 1,5 2,5 3,5 4,5 6,5 5,1 5,2 5,3 5,4 5,6

probability of getting 5 at least once=10/36 = 5/18

2(4)

favorable outcome=5,5

probability of getting 5 on both the dice=1/36

last question is wrong

but hope that the answers for the others helped u ;)