Tom and Jerry play one game per day. It is known that Tom's winning chance is P[W]=0.6 and if he does not win then he loses. Game results are assumed to be independent. AFter 4 days, variable T indicates a total number of games won by Tom. So J=4-T is the number of games he lost (or Jerry won)
1. Find the chance that Tom loses exactly one game P(J-1)
To find the chance that Tom loses exactly one game, P(J-1), we first need to determine the probability of Tom losing one game, P(L), and then multiply it by the probability of Tom winning the remaining three games, P(W)^3.
The probability that Tom loses one game, P(L), can be calculated as the complement of Tom winning one game, P(W)=0.6. So, P(L) = 1 - P(W) = 1 - 0.6 = 0.4.
Now, we can calculate the probability of Tom losing exactly one game, P(J-1), as follows:
P(J-1) = P(L) * P(W)^3 = 0.4 * (0.6)^3 = 0.4 * 0.216 = 0.0864
Therefore, the chance that Tom loses exactly one game is 0.0864 or 8.64%.