A flashlight has 8 batteries out of which 3 are dead. If two batteries selected without replacement and tested, then probability that both are dead is

Correct option is: D) \((\frac{3}{x+3})(\frac{x}{x-2})\)

Let `E_(1)`=Event that first ball being red and `E_(2)`= Event that exactly tw of the three balls being red `therefore P_(E_(1))=P_(R)cdotP_(R)cdotP_(R)+P_(R)cdotP_(R)cdotP_(barR)+P_(R)cdotP_(barR)cdotP_(R)+P_(R)cdotP_(barR)cdotP_(barR)`

Required probability=`4/52cdot4/52=1/13xx1/13`

Here, n=5,p`=10/100=1/10andq=9/10` `rle1` `rArrr=0,1` Also, `P(X=r)=""^(n)C_(r)p^(r )q^(n-r)` `therefore P(X=r)=P(r=0)+P(r=1)` `=""^(5)C_(0)(1/10)^(0)(9/10)^(4)` `=(9/10)^(5)+5cdot1/10cdot(9/10)^(4)` `(9/10)^(5)+1/2(9/10)^(4)`

Correct Answer - Not possible P(A) = 0.5, `P(A nn B) le 0.3` So, `P(A uu B) = P(A) + P(B) - P(A nn B)` gives `P(B) = P(A uu B)...

Correct Answer - D Three-digit numbers are 100, 101, …, 999. Total number of such numbers is 900. The three-digit numbers (which have all same digits) are 111, 222, 333, …,...

Correct Answer - A::B::C Here total number of cases is `.^(8)C_(2) = 28` 1. Number of favorable case is 13. For 2 `rarr` 6 choices For 1 `rarr` 7 choices 2....

Let A nad B denote, respectively, the events that first ball drawn is black and second ball drawn in white. We have to find `P(AnnB) or P(AB).` ` P(AnnB)P(A)P(B//A)` Now,...

Correct Answer - `1/7` Required probability `=P(WBWB)+P(BWBW)` `=P(W)P(B//W)P(W//WB)P(B//BWB)` `=5/8xx3/7xx4/6xx2/5+3/8xx5/7xx2/6xx4/5` `=(1)/(14)+(1)/(14)=1/7`

Correct Answer - A `S={00,01,02,....,49}` Let A be the event that the sum of the digits on the selected ticket is 8. Then `A={08,17,26,35,44}` Let B be the event that the...