7. Five mark exercise problems - I

1. If \(A\) is an event of a random experiment such that \(P(A) : P(\overline A) = 17 : 15\) and \(n(S) = 640\) then find (i) \(P(\overline A)\) (ii) \(n(A)\).

 

Answer:

 

(i) \(P(\overline A) =\) $\frac{i}{i}$

 

(ii) \(n(A) =\)

 

2. At a fete, cards bearing numbers \(1\) to \(1000\), one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than \(500\), the player wins a prize. What is the probability that (i) the first player wins a prize (ii) the second player wins a prize, if the first has won?

 

Answer:

 

(i) The first player wins a prize \(=\) $\frac{i}{i}$

 

(ii) The second player wins a prize, if the first has won \(=\) $\frac{i}{i}$

 

3. A bag contains \(12\) blue balls and \(x\) red balls. If one ball is drawn at random (i) what is the probability that it will be a red ball? (ii) If \(8\) more red ball will be twice that of the probability in (i), then find \(x\).

 

Answer:

 

(i) The probability that the ball drawn is a red ball \(=\) $\frac{i}{i}$

 

(ii) The value of \(x =\)