1. A pizza parlor has 12 different toppings available for its pizza; and 2 of th
ID: 3332969 • Letter: 1
Question
1. A pizza parlor has 12 different toppings available for its pizza; and 2 of these toppings are at random, find the probability pepperoni and anchovies. If a customer picks two toppings that (a) neither topping is anchovies? 4 (b) pepperoni is one of the toppings? [4] 2. Consider rolling a pair of dice two times, let A and B be the total on the up-faces. For each of the following pairs of events, tell whether they are disjoint, independent, or neither (a) A-12 on the first roll), B = {8 or more on the first roll). [2] (b) A-2 on the first roll), B = {8 or more on the second roll). [2] (c) A- 15 or less on the second roll), B- [4 or less on the first roll). [2] (d) A-[5 or less on the second roll, B 14 or less on the second roll). [2] 3. Here is probability distribution for a random variable X: Probability 0.20.8 (a) Find the mean and standard deviation for Y - 5X -1 [6] (b) Find the mean and standard deviation for T-5X2-1 [8] About 1 percent of women have breast cancer. A cancer screening method can detect 8 percent of genuine cancers with a false alarm rate of 10 percent. What is the probability that women producing a positive test result really have breast cancer. [12Explanation / Answer
Ans:
1)a)Probability of not choosing anchovies is =11/12
P(neither is anchovies)=(11/12)*(11/12)=121/144=0.84
b)P(one of the topping is pepperoni)=(1/12)+(1/12)=2/12=1/6
4)P(cancer)=0.01
P(positive/cancer)=0.8
P(postive/not cancer)=0.1
P(cancer/positive)=P(positive/cancer)*P(cancer)/[P(positive/cancer)*P(cancer)+P(positive/not cancer)*P(not cancer)]
=0.8*0.01/[0.8*0.01+0.1*0.99]
=0.008/0.107
=0.0748
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