In a national tournament the probability of Pramod to get Gold medal is 0.4 . The probability of Gunjan to get Gold medal is 0.5 . The probability of Samir to get Gold medal is 0.6 . The probability of Suresh to get medal is 0.8 . What is the probability that at least 2 of the got gold medal on that day?
a. 0.632
b. 0.732
c. 0.688
d. 0.806
Answers
Answer:
option D: (0.806)
Explanation:
P=Pramod, G=Gunjan, S=Samir, Su=Suresh
P(P getting gold)=0.4
P(G getting gold)=0.5
P(S getting gold)=0.6
P(Su getting gold)=0.8
P(P not getting gold)= 1-0.4 = 0.6
P(G not getting gold)= 1-0.5 = 0.5
P(S not getting gold)= 1-0.6 = 0.4
P(Su not getting gold)= 1-0.8 = 0.2
P (at least 2 of them got a gold medal) = 1- [P(none getting a gold medal or Only one of them getting a gold medal)
= 1 - (none getting) - (P getting) - (G getting) - (S getting) - (Su getting)
= 1 - (0.6)(0.5)(0.4)(0.2) - (1-0.6)(0.5)(0.4)(0.2) - (0.6)(1-0.5)(0.4)(0.2) - (0.6)(0.5)(1-0.4)(0.2) - (0.6)(0.5)(0.4)(1-0.2)
= 1- (0.6)(0.5)(0.4)(0.2) - (0.4)(0.5)(0.4)(0.2) - (0.6)(0.5)(0.4)(0.2) - (0.6)(0.5)(0.6)(0.2) - (0.6)(0.5)(0.4)(0.8)
= 1 - 0.024 - 0.016 - 0.024 - 0.036 - 0.096
= 1 - (0.024 + 0.016 + 0.024 + 0.036 + 0.096)
= 1 - (0.196)
= 0.804
P(at least 2 of them got a gold medal) = 0.804
(The option seems to have got mistaken for 0.804 as 0.806)