4 I en påse finns 3 röda och 5 gula kulor. Du tar en kula ur påsen utan att titta, noterar färgen och lägger tillbaka kulan. En ny kula tas upp pả samma sätt. Beräkna med hjälp av ett träddiagram \( \begin{array}{ll}\text { a) } P(2 \text { gula kulor }) & \text { b) } P(2 \text { röda kulor) } \\ \text { c) } P(1 \text { röd och } 1 \text { gul kula }) & \text { d) } P(\text { minst en röd kula })\end{array} \)

a) 3 pts: Colauler \( P(A \cap B) \)

A student takes an exam containing 16 true or false questions. At least 11 correct answers are required to pass. If the student guesses, what is the probability that he will pass? Round your answer to the nearest ten-thousandth, if necessary. Answer

Two dice of the colours red and blue are thrown. (a) Write the sample space in ordered pair form. (b) Find the probability of getting; (i) 1 on blue die or 6 on red die (ii) 3 on blue die or 5 on red die (c) Show the sum of the elements of each ordered pair (d) Calculate the probability of getting;

Question 4 of 15 , step 1 of 1 A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. If the number of defective bulbs is 2 or more, the lot fails inspection. Suppose \( 30 \% \) of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to the nearest ten-thousandth, if necessary. Answer

The probability density function of random variable \( X \) is given by: \[ f(x)=\left\{\begin{array}{cc}k e^{x+1}, & -2 \leq x \leq 2 ; \\ 0, & \text { otherwise. }\end{array}\right. \] Then \( k \) is equal to: