Answer to Question #121817 in Statistics and Probability for kantish

Question

Pakistan Cricket Board in its central contract places its International players in four different categories, Category A, Category B, Category C and Emerging Players’ Category. Batsmen who are going to play in upcoming series fall into these four categories in the proportions 30 percent, 40 percent, 20 percent and 10 percent. The probability that a Category A player will get out without scoring a single run is 0.01, for Category B player its 0.04, for Category C player its 0.12 and the probability that an emerging player will get out on Zero is 0.06.

During a match after the fall of second wicket captain sent Muhammad Rizwan on batting and he got out on Zero. What is trhe probability that Muhammad Rizwan is;

a) In Category A b) In Category B c) In Category

Answer 1

P(A)=0.30 

P(B)=0.40

P(C)=0.20 

P(Emerging)=0.10 

P(without scoring∣A)=0.01

P(without scoring∣B)=0.04

P(without scoring∣C)=0.12 

P(without scoring∣Emerging)=0.06

a)P=P(A)*P(without scoring∣A)/(P(A)*P(without scoring∣A)+P(B)*P(without scoring∣B)+P(C)*P(without scoring∣C)+P(Emerging)*P(without scoring∣Emerging))=(0.30 *0.01)/(0.30 *0.01+0.40*0.04+0.20 *0.12 +0.10 *0.06)=0.003/0.049=0.061

b)P=P(B)*P(without scoring∣B)/(P(A)*P(without scoring∣A)+P(B)*P(without scoring∣B)+P(C)*P(without scoring∣C)+P(Emerging)*P(without scoring∣Emerging))=(0.30 *0.01)/(0.30 *0.01+0.40*0.04+0.20 *0.12 +0.10 *0.06)=0.016/0.049=0.3265

c)P=P(C)*P(without scoring∣C)/(P(A)*P(without scoring∣A)+P(B)*P(without scoring∣B)+P(C)*P(without scoring∣C)+P(Emerging)*P(without scoring∣Emerging))=(0.30 *0.01)/(0.30 *0.01+0.40*0.04+0.20 *0.12 +0.10 *0.06)=0.024/0.049=0.49