Tickets for an event are allocated randomly from those who apply. For each of three events 1,000 apply for 500 tickets. 16 friends each apply separately for each of the three events.Question 20What is the expected number of the 16 friends who will get tickets for all three events?1234
Question
Tickets for an event are allocated randomly from those who apply. For each of three events 1,000 apply for 500 tickets. 16 friends each apply separately for each of the three events.Question 20What is the expected number of the 16 friends who will get tickets for all three events?1234
Solution
To solve this problem, we first need to calculate the probability of a single friend getting a ticket for one event. Since there are 500 tickets for 1000 applicants, the probability is 500/1000 = 0.5.
Next, we need to find the probability of a single friend getting tickets for all three events. Since the events are independent, we multiply the probabilities together: 0.5 * 0.5 * 0.5 = 0.125.
Finally, we need to find the expected number of friends who will get tickets for all three events. We do this by multiplying the probability by the number of friends: 0.125 * 16 = 2.
So, the expected number of the 16 friends who will get tickets for all three events is 2.
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