[left]Two important members of a cricket team are injured, and each has probability 1/3 of recovering before the match. The recoveries of the two players are independent of each other. If both are able to play then the team has probability 3/4 of winning the match, if only one of them plays then the probability of winning is 1/2 and if neither play the probability of winning is 1/16. What is the probability that the match is won?

Hi there.

probability(no one recovers and the game is won) = 2/3 * 2/3 *1/16

prob(one guy recovers and the game is won) = 2/3*1/3 * 1/2 + 1/3 * 2/3 *1/2

prob(everyone recovers and the game is won) = 2/3*2/3 * 3/4

prob("game is won")=2/3 * 2/3 *1/16 + 2/3*1/3 * 1/2 + 1/3 * 2/3 *1/2 + 2/3*2/3 * 3/4

i just added all three probabilities and i got prob() = 0.5833....3

There are two mistakes in the above. It should be:
prob(everyone recovers and the game is won) = 1/3*1/3 * 3/4