Probability - 5

Q. 6- In a bag 4 cards morked with 'I' and. 4 marked with 'T' are present . 3 time a card is drawn without .

replacement. Find the chance of forming wird 'I I T'.

Ans - Total no. of way
= n(S) = 8C₃
drawing 3 cards

n(A) = 4C₂ X 4C₁

P(E)=

Dumb question :-

How does n(A) = 4C₂ X 4C₁ ?

Ans:- For wird 'I I T' we reguire 2I'_s and I 'T' So, out of 4 I' s we require 2 I' _s and out of 4 T'_s ,we require 1 T. So, n(A) = 4C₁

Q. 7 - Probability of a no. appearing if a clice is rolled is proportipnal lto the ,no. Find the chance of getting aprime no ?

Ans- Probability . P(1) = P(2) = 2

P(3) = 3 P(4) = 4 P(5) = 5

P(6) = 6

P(1) probability of getting 1 if clice is ralled

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) =

= 21

But 21 = 1 total prabability



P(prime) = P(2) + P(3) + P(5) = 10

Q. 8 - A Coin is tossed l4 time if head appeared 1 point awarded and tail appeared 2 point given. Find expectation of player ?

Ans- P(4) = P(HHHH) =

P(5) = P ( HHHT/HHTH/HTHH/THHH )

= 4 X

=

P(6) = P (HHTT/HTHT/HTTH/TTHH/THTH/THHT)

= 6 X ( 1/2 X 1/2 X 1/2 X 1/2 X )

= 6/16

P(7) = P(HTTT/THTT/TTHT/TTTH )

= 4 x

P(8) = P(TTTT) =

P(4) probability of getting 4 points.

Expectation =

= [ 4 + 20 + 36 + 28 + 8 ]

=

Dumb question :- What is expectati0n ?

Ans - If P be probability of success of a person in any event and M be prize money which be will receive in case of sussess, themn,

Expectation = PM = probability of success X prize money

Q. 9- There are 3 compartment in a box. A ball is randomly drawn from anyone compartment. Find chance it is ded



Ans - E₁ frawn from I_st compartment

E₂ frawn from II_nd compartment

E₃ frawn from III_rd compartment

E . bll is red

P( E₁ ) = P( E₃ ) = 1/3 ( equally likely event )



P(E) = P( E img E₁) + P( E img E₂) + P( E img E₃)

= P( E₁ ) P( E / E₁ ) + P( E / E₂ ) + P( E / E₂ ) + P( E/E₃ ). P( E / E₃ ) = 3 / 7

P(E) =

Q. 10 A coin is tossed till head and tail appears, it can be tossed 5 time max . First 2 throws are H H . Find the chance that coin tossed 5 time.?

Ans- I^st two throws are H H and if 3 ^rd and 4^th throw are also H H . So we have to go for 5^th throw for getting tail.



P(A) =