Maths Probability 2question

Q1. if two card are drawn randomly
All of choices will be 5C2=10

(the first card, get 1 from 5 cards
the second card, get 1 from 4 cards
but we dont care the order (which one is first or second)
so the choice= (5X4)/2=10 )

if the sum of the cards is 5, (2,3) and (2, another3)
choice=2

so the first answer is 2/10=1/5


Q2

he shoot, he hit the target probability is 2/3
if the shoot doesn't work, the probablilty 1/3

(1).if the first shoot doesn't work, but the second shoot works, the probability (1/3)X(2/3)=2/9

(2).if the first shoot works but the second shoot doesn't work, the probability (2/3)X(1/3)=2/9

(3).if he can shoot correct at two choice (2/3)x(2/3)=4/9

so at least he can shoot one probability is (1)+(2)+(3)=(2/9)+(2/9)+(4/9)=8/9

or other method,

if one of shoot succeed, the probability is2/3, whatever another works or not
if the one doesn't work but another does, the probability is (1/3)X(2/3)=2/9

so the total probability is (2/3)+(2/9)=8/9

1)
1/5 x 2/5 + 2/5 x 1/5 = 4/25
2)
1/3 x 2/3 + 2/3 x 1/3 + 2/3 x 2/3 = 8/9
or simply, 1-(1/3 x 1/3) = 8/9

1.Make a table of the sum of every card you draw. Please be reminded that the cards are drawn without replacement. Therefore, the same card shoud only be drawn once.
Possible outcome = 20
Favourable outcome = 4
Probability=4/20=1/5

Therefore, the probability that the sum of the numbers on the card drawn is 5 is 1/5(A).

2.There are 2 ways to do that.
First Method:
1-probability that he doesn't hit the target at the 2 times he shoots
= 1- 1/3*1/3
=8/9

Second Method:
probability that he hits at the first shoot but fails at the second + probability that he fails at the first shoot but hits at the second + probability that he hits both targets
=2/3*1/3+1/3*2/3+2/3*2/3
=2/9+2/9+4/9
=8/9

Therefore, the answer is E.

1. If the sum of the numbers on the cards drawn is 5,
means two cards are 2+3 or 3+2

Probability of 2+3 is, (2/5)(1/4)=2/20=1/10
Probability of 3+2 is, (1/5)(2/4)=2/20=1/10

Therefore, (Probability of 2+3) + (Probability of 3+2) = 1/10+1/10 = 2/10 = 1/5
Answer (A).

2. P(Hit)xP(Miss)+P(Miss)xP(Hit)+P(Hit)xP(Hit)
(2/3)(1/3)+(1/3)(2/3)+(2/3)(2/3)
=(2/9)+(2/9)+(4/9)
=8/9

Therefore, the answer is E. 8/9