There are 3 cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be selected at random with replacement. Using a tree diagram, obtain the sample space for the experiment. Then, find the probability that you choose the same card twice. Round to 4 decimals when necessary.

The PMF of a random variable \( X \) taking value in \( N \cup\{0\} \) is given by \( P_{I}(i)=e^{-\lambda} \frac{\lambda^{i}}{n}, i=0,1,2, \ldots \) where \( \lambda \) is a positive real number. Given that \( \lambda=2 \), find \( P(X=0) \) \( P(X>2) \)

The PMF of a random varlable \( X \) taking value in \( N \cup\{0\} \) is given by \( P_{I}(i)=e^{-\lambda} \frac{\lambda^{i}}{n}, i=0,1,2, \ldots \) where \( \lambda \) is a positive real number. Given that \( \lambda=2 \), find \( P(X=0) \) \( P(X>2) \)

Dr Faridon Amdjadi, Mechanical Engineerin Find the probability \( P(-1.15<z<0.09) \) using the standard normal distribution. Select the correct answer. 0.5894

(b) If an output component is only accepted when its length lies in the range between 112.8 mm and 168.0 mm , find the expected proportion of components that are accepted i.e. determine the below probability Enter your answer rounded correct to 4 decimal places \( P(112.8<X<168.0)= \) Number (7.5 Mark) Click on Verity to continue Section Attempl 1 of 1

Dr Faridon Amdjadi, Mechanical Engineering (Tota Find the probability \( P(-1.24<z<-0.07) \) using the standard normal distribution. Select the correct answer. 0.6464 0.6823 0.1841 0.3646