Multiple Choice Exam & Jelly Beans in a Bag

Probability drives me crazy (Headbang)

I couldn't figure out how it solves(Worried)(Worried)

could you help me please (Itwasntme)

Multiple Choice Exam

Each question on a 5 questions multiple choice examination has 4 choices,only one of which is correct . If a student answers each question on a random fashion, what's the probability that the student answers exactly 2 question incorrectly ?

My answer :

#$\displaystyle (S)=1024 (4^5)$

#$\displaystyle (E)=10 (5C3)$ I said if the student answers 2 question incorrectly is the same as if he answers ignore any 2 question

$\displaystyle P(E)= 10/1024$

tell me how to solve it plz

BUT the right answer is ($\displaystyle 45/512$)

Jelly Beans in a Bag

Abag contains 4 red and 6 green jelly beans.

a) if 2 jelly beans are randomly selected in succession with replacement, determine the probability that both are red.

b)if the selection is made without replacement .determine the probability that both are red.

My answer

#($\displaystyle S)=24$

a)#$\displaystyle (E)= 4c2

P(E)= 6/24=1/4

$

b)#($\displaystyle E)= 4p2

P(E)= 12/24=1/2

$

BUT the right answer is

$\displaystyle a)4/25

$

$\displaystyle

b)2/15

$

Tell me please how to solve them

:(

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