Math115a Conditional Probability #1 Name:________________________ReyesUse any method to solve but show all work for credit. Define all random variables used and use the correct mathematical notation. 1. The probability that event A occurs is .63. The probability that event B occurs is .45. The probability that both events A and B occur is .18. Find the following: a.( )P A Bb.( )P B Ac. Are the events independent?2. Two fair dice are rolled. Find the probability that the sum rolled is at least ten, given: a. No information at all b. At least one die comes up six c. The same number appears on both dice3. A family has three children. Find the probability of having two boys, given that at most one of the children are girls.4. In a small town the given chart below reflects the ethic and religious backgrounds of the townsmen. Let C, B, I, and S denote the events of being Catholic, Baptist, Italian, and Spanish respectively. Religion/Ethnic backgroundItalian Spanish TotalCatholic 145 122 267Baptist 111 225 336Total 256 347 603Find the following: a.( )P Bb.( )P C I c.( )P S
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