Consider randomly selecting a student at a certain university, and let ?A ?denote the event that the selected individual has a Visa credit card and ?B ?be the analogous event for a MasterCard. Suppose that P(A)=.5. P(B)= .4. and P(A ?B) =25. a?. ?Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event (A ?B). b?. ?What is the probability that the selected individual has neither type of card? c. ?Describe, in terms of ?A ?and ?B, ?the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.

Answer Step 1 of 5 From the given data find relative frequencies and densities values frequency Relative frequencies Frequency density 3.0-<3.5 5 5/131=0.038 5/5=1 3.5-<4.0 15 15/131=0.115 15/5=3 4.0-<4.5 27 27/131=0.206 27/5=5.4 4.5-<5.0 34 34/131=0.26 34/5=6.8 5.0-<5.5 22 22/131=0.168 22/5=4.4 5.5-<6.0 14 14/131=0.107 14/5=2.8 6.0-<6.5 7 7/131=0.053 7/5=1.4 6.5-<7.0 2 2/131=0.015 =0.4 7.0-<7.5 4 4/131=0.031 =0.8 7.5-<8.0 1 1/131=0.008 =0.2 total 131 1 Step 2 of 5 The proportion of the observations are less than 5=0.038+0.115+0.206+0.26=0.619 Step 3 of 5 The proportion of the observations are at least 6 = 0.053+0.015+0.031+0.008=0.107