Question

. ​Ravi plays a game in which he has to draw one ball from a box containing 3 Red, 4 white and 3 green balls. On drawing a white ball Ravi is rewarded with Rs. 10. On drawing a red ball Ravi is to pay a penalty of Rs.5 and in other cases there neither any reward nor penalty. Find (i) P (Ravi is rewarded Rs. 10) (ii) P (Ravi does not lose) (iii)P (Ravi pays a penalty of Rs. 5)

Answer 1

P(Ravi is rewarded Rs. 10) = 0.4

P(Ravi does not lose) = 0.7

P(Ravi pays a penalty) = 0.3

Explanation:

Step 1 :

Probability of any event happening = Total number of favorable outcomes / Total number of outcomes

Step 2 :

(i) P (Ravi is rewarded Rs. 10) = P(Ravi selecting a white ball)

Total number of favorable outcomes = Total number of white balls = 4

Total number number of outcomes = 10

Probability of selecting a white ball = Total number of white balls/Total number of outcomes =4/10 = 0.4

Hence P (Ravi is rewarded Rs. 10) = 0.4

Step 3 :

(ii) P (Ravi does not lose)

Probability of Ravi not losing is probability of Ravi not selecting a Red ball [ because Ravi has to pay penalty only when he chooses red ball

P(Ravi selecting Red ball) = Total number of red balls/Total number of outcomes =3/10 = 0.3

Hence P (Ravi does not lose) = 1-0.3 = 0.7

Step 3 :

(iii)P (Ravi pays a penalty of Rs. 5)

P (Ravi pays a penalty of Rs. 5)= Ravi selecting a Red ball

P(Ravi selecting Red ball) = Total number of red balls/Total number of outcomes =3/10 = 0.3

Hence P (Ravi pays a penalty of Rs. 5) = 0.3