In a restaurant seventy percent of people order for Chinese food and thirty perc
ID: 3252875 • Letter: I
Question
In a restaurant seventy percent of people order for Chinese food and thirty percent for Italian food. A group of three persons enter the restaurant. a. Find the probability of at least two of them ordering for Italian food. 0.27 0.9998 0.05 0.08765 Radioactive atoms are unstable because they have too much energy. When they release their extra energy, they are said to decay. When studying cesium-137, it is found that during the course of decay over 365 days, 1,000,000 radioactive atoms are reduced to 977, 287 radioactive atoms. a. Find the mean number of radioactive atoms lost through decay in a day. 0.2347 134,000 0.8745 22, 713 b. Find the probability that on a given day, 50 radioactive atoms decayed. 0.0155 0.2225 0.9999 0.6543Explanation / Answer
The probability of ordering Chinese food is 0.7 and the probability of ordering Italian food is 0.3. Now, if at least two of them are ordering Italian food then it implies that either two or three will order Italian food.
Probability for two ordering Italian food,
P(X=2)P(X=2) = 23C(0.3)2(0.7)132C(0.3)2(0.7)1
= 3×0.09×0.73×0.09×0.7
= 0.1890.189
Probability for all three ordering Italian food,
P(X=3)P(X=3) = 33C(0.3)3(0.7)033C(0.3)3(0.7)0
= 1×0.081×11×0.081×1
= 0.0810.081
Hence, the probability for at least two persons ordering Italian food is,
P=P(X=2)+P(X=3)P=P(X=2)+P(X=3)
= 0.189+0.081=0.27
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